5-1. Rate of Change and Slope. Vocabulary. Review. Vocabulary Builder. Use Your Vocabulary

Transcription

1 - Rate of Change and Slope Vocabular Review. Circle the rate that matches this situation: Ron reads books ever weeks. weeks books. Write alwas, sometimes, or never. A rate is a ratio. books weeks books weeks A ratio is a rate.. Underline the correct word to complete each sentence. A rate compares two quantities b division / multiplication. A rate compares quantities in different / the same unit(s). Vocabular Builder slope (noun) slohp Definition: Slope is the ratio of the vertical change (or rise) to the horizontal change (or run) between two points on a line. Slope is also called the rate of change. Main Idea: Slope describes the steepness of a line in the coordinate plane. Eamples: You can measure the slope of a hill, mountain, road, or roof. Use Your Vocabular. How does the slope of a road affect a person s driving?. What kind of ski slope would a beginner skier use? vertical change rise slope horizontal change run Chapter

2 Problem Finding Rate of Change Using a Table Got It? The table at the right shows the distance a band marches over time. The rate of change from one row of the table to the net is feet per minute. Do ou get the rate of change of feet per minute if ou use nonconsecutive rows of the table? Eplain.. Use the values from the second and fourth rows to find the rate of change. change in distance rate of change change in time Distance Marched Time (min) Distance (ft) When ou use nonconsecutive rows, the rate of change is ft per min.. Is the rate of change ou found in Eercise the same as if ou had used two consecutive rows? Eplain wh or wh not. Problem Finding Slope Using a Graph Got It? What is the slope of the line?. Label each point on the graph with its coordinates.. Draw a vertical arrow to represent the rise. rise. Draw a horizontal arrow to represent the run. run. Underline the correct word(s) to complete the sentence. Because the points are on the same line, the rate of change from point to point is constant / differs.. Write the slope of the line. vertical change slope horizontal change rise run O Lesson -

3 Ke Concept The Slope Formula In the diagram, (, ) are the coordinates of point A, and (, ) are the coordinates of point B. To find the slope of * AB ), ou can use the slope formula. slope rise run, where B(, ) A(, ) When using the slope formula, the coordinate ou use first in the denominator must belong to the same ordered pair as the coordinate ou use first in the numerator.. To find the change in or coordinates, do ou add or subtract?. What number will ou get in the denominator if the -coordinates are the same? Eplain how that will affect the answer ou find for the slope. Problem Finding Slope Using Points Got It? What is the slope of the line through (, ) and (, )?. You can use either pair for (, ). For eample, use (, ) for (, ). Then use (, ) for (, ).. Complete the equation. slope Problem. The slope of the line through (, ) and (, ) is. Finding Slopes of Horizontal and Vertical Lines Got It? What is the slope of the line through (, ) and (, )?. Graph the points (, ) and (, ) and draw the line that goes through the points.. Is the line that ou drew horizontal or vertical?. What is the slope of the line through (, ) and (, )? O Chapter

4 Concept Summar Slopes of Lines. Label each graph with one of the descriptions below. negative slope positive slope slope of undefined slope O O O O Lesson Check Do ou UNDERSTAND? Compare and Contrast How does finding a line s slope b counting units of vertical and horizontal change on a graph compare with finding it using the slope formula?. Describe how the two methods of finding slope are the same.. Describe how the two methods of finding slope are different. Math Success Check off the vocabular words that ou understand. rate of change Need to review slope Rate how well ou can find the slope of a line. Now I get it! Lesson -

5 Name Class Date - Think About a Plan Rate of Change and Slope Profit John s business made $ in Januar and $ in March. What is the rate of change in his profit for this time period? Understanding the Problem. What is the formula for finding rate of change?. What are the two changing quantities that affect rate of change in this problem? What are the units of each quantit?. Will the rate of change be positive or negative? Eplain. Planning the Solution. Which quantit is the dependent variable? Which quantit is the independent variable? Eplain.. What is the general equation that represents the rate of change? Getting an Answer. Substitute values into our general equation and simplif. Show our work.. If ou were to graph this relationship, what would the rate of change be in relation to our graph? Chapter

6 Name Class Date - Practice Form K Rate of Change and Slope Each rate of change is constant. Find the rate of change and eplain what it represents.. Fences Painted. Hours Fences Miles Per Hour Hours Miles Find the slope of each line... O O.. O O Find the slope of the line that passes through each pair of points.. (, ), (, ). (, ), (, ). (, ), (, ). (, ), (, ) Find the slope of each line... O O Lesson -

7 Name Class Date - Practice (continued) Form K Rate of Change and Slope Without graphing, tell whether the slope of a line that models each linear relationship is positive, negative, zero, or undefined. Then find the slope.. The cost of a pair of jeans is $. for pair and $. for pairs.. An emploee earns $. after hours and $. after hours. State the independent variable and the dependent variable in each situation. Then find the rate of change for each situation.. The cost of three gallons of milk is $. and five gallons of milk is $... Jacques filled envelopes in minute and envelopes in minutes. Find the slope of the line that passes through each pair of points.. (, ), (, ). (, ), (., ). Q, R, Q, R. Q, R, Q, R. Writing Eplain wh the slope of a vertical line is alwas undefined.. Writing Describe how to draw a line that passes through the origin and has a slope of. Each pair of points lies on a line with the given slope. Find or.. (, ), (, ); slope. (, ), (, ); slope Chapter

8 Name Class Date - Standardized Test Prep Rate of Change and Slope Multiple Choice For Eercises, choose the correct letter.. What is the slope of the line that passes through the points (, ) and (, )? A. B. C. D.. A line has slope. Through which two points could this line pass? F. (, ), (, ) H. (, ), (, ) G. (, ), (, ) I. (, ), (, ). The pair of points (, ) and (, ) lie on a line with slope. What is the value of? A. B. C. D.. What is the slope of a vertical line? F. G. H. I. undefined. Shawn needs to read a book that is pages long. The graph shown at the right shows his progress over the first hours of reading. If he continues to read at the same rate, how man hours total will it take for Shawn to read the entire book? A. hours C. hours B. hours D. hours Short Response. Robi has run the first miles of a race in minutes. She reached the mile point after minutes. Without graphing, is the slope of the line that represents this situation positive, negative, zero, or undefined? What is the slope? Pages Read (, ) (, ) O Hours Reading Lesson -

9 - Direct Variation Vocabular Review. Cross out the epression below that does NOT show a formula for slope. horizontal change vertical change. Underline the correct word in each sentence about slope. rise run The slope of a horizontal line is undefined / zero. The slope of a vertical line is undefined / zero. Vocabular Builder direct (adjective) duh REKT Definition: Direct means straightforward in language or action. k, where k, is a direct variation. In the above, k is called the constant of variation. Other Word Forms: directl (adverb), direction(s) (noun) Math Usage: If the ratio of two variables is constant, then the variables form a direct variation. What It Means: In a direct variation, one variable directl affects another b multipling it b a constant value. Both variables decrease: The more epensive the car, the more sales ta ou pa. One variable increases, the other variable decreases: As a candle burns longer, its height gets smaller. Use Your Vocabular Choose the correct word from the list to complete each sentence. directl direct directions. Renee gave the visitor to the museum.. The fans went to their seats.. There is a connection between the outside temperature and the number of people at the beach. Chapter

10 A function in the form k, where k, represents a direct variation. The constant of variation k is the coefficient of. To determine whether an equation represents a direct variation, solve it for. If ou can write the equation in the form k, where k, it represents a direct variation. Problem Identifing a Direct Variation Got It? Does represent a direct variation? If so, find the constant of variation.. Circle the equation that shows direct variation. k k k. Complete the steps to solve for. Write the original equation. Subtract from each side. Divide each side b.. Does represent a direct variation? Eplain.. In the equation, is the constant of variation. Problem Writing a Direct Variation Equation Got It? Suppose varies directl with, and when. What direct variation equation relates and? What is the value of when?. Complete the reasoning model below. Think Write I start with the function form of direct variation. Then I substitute for and for. Now I divide each side b to solve for k. Net, I write an equation b substituting for k. Finall, I determine the value of when. ( ) Lesson -

11 Problem Graphing a Direct Variation Got It? Weight on the moon varies directl with weight on Earth. A person who weighs lb on Earth weighs. lb on the moon. What is an equation that relates weight on Earth and weight on the moon? What is the graph of this equation?. Find the value of k. Round k to the nearest hundredth if necessar. k k? k. To the nearest hundredth, k. So, <?.. Make a table of values.. Graph the values from the table. O Concept Summar Graphs of Direct Variations The graph of a direct variation equation k is a line with the following properties. The line passes through (, ). The slope of the line is k.. Substitute and in the equation.? k. Because the graph of passes / does not pass through (, ), the k equation is / is not a direct variation. Chapter

12 Problem Writing a Direct Variation From a Table Got It? For the data in the table at the right, does var directl with? If it does, write an equation for the direct variation.. Write each ordered pair as the ratio of the -coordinate to the -coordinate. Then write the ratio of to as a decimal. (,.) (,.) (, )... For the data in the table, does var directl with? Yes / No. The equation for the direct variation shown is?. Lesson Check Do ou UNDERSTAND? Vocabular Determine whether each statement is alwas, sometimes, or never true. The ordered pair (, ) is a solution of the direct variation equation k.. Substitute (, ) into k.. The statement is true. k? You can write a direct variation in the form k, where k u.. Is k of the form k?. The statement is true. Math Success Need to review Yes / No The constant of variation for a direct variation represented b k is.. When ou divide each side of k. Because ou cannot divide b, b, ou obtain k. the statement is true. Check off the vocabular words that ou understand. direct variation Rate how well ou can work with direct variation. constant of variation for a direct variation Now I get it! Lesson -

13 Name Class Date - Think About a Plan Direct Variation Electricit Ohm s Law V I R relates the voltage, current, and resistance of a circuit. V is the voltage measured in volts. I is the current measured in amperes. R is the resistance measured in ohms. a. Find the voltage of a circuit with a current of amperes and a resistance of ohms. b. Find the resistance of a circuit with a current of amperes and a voltage of volts. Understanding the Problem. Does Ohm s Law represent a direct variation? Eplain.. If the formula is rearranged to solve for R or I, is it still a direct variation? Eplain. Planning the Solution. For part (a), does Ohm s Law need to be rearranged to answer the question? Eplain. If it does, how should the formula be rearranged?. For part (b), does Ohm s Law need to be rearranged to answer the question? Eplain. If it does, how should the formula be rearranged? Getting an Answer. For part (a), substitute the given values into the formula and simplif.. For part (b), substitute the given values into the formula and simplif. Chapter

14 Name Class Date - Practice Form K Direct Variation Determine whether each equation represents a direct variation. If it does, find the constant of variation..... Suppose varies directl with. Write a direct variation equation that relates and. Then find the value of when.. when. when. when.. when. Graph each direct variation equation..... The perimeter of a square varies directl with the length of one side. What is an equation that relates the perimeter p and length l of the side? What is the graph of the equation? Lesson -

15 Name Class Date - Practice (continued) Form K Direct Variation For the data in each table, tell whether varies directl with. If it does, write an equation for the direct variation Write a direct variation equation that relates and. Then graph the equation.. when. when Tell whether the two quantities var directl. Eplain our reasoning.. Sara makes $. more per hour than Pasco.. The cafeteria provides three meals per da.. Jasmine scores points per game.. Reasoning How can ou tell, b eamining the graph, if a line represents a direct variation? Chapter

16 Name Class Date - Standardized Test Prep Direct Variation Gridded Response Solve each eercise and enter our answer on the grid provided.. Suppose varies directl with and when. What is the value of when?. Suppose varies directl with and when. What is the value of when?. The point (, ) is included in a direct variation. What is the constant of variation?. The equation of the line on the graph at the right is a direct variation equation. What is the constant of variation?. The distance d a train travels varies directl with the amount of time t that has elapsed since departure. If the train travels miles in. hours, how man miles did the train travel after hours?..... O Lesson -

17 - PART Slope-Intercept Form Vocabular Review. Multiple Choice Which equation is NOT a linear equation?. Place a in the bo if the statement applies to the graph of a linear equation. Place an if it does NOT appl to the graph of a linear equation. The graph of a linear equation is alwas a horizontal line. The graph of a linear equation is alwas a straight line. The graph of a linear equation ma be shaped like a U. Vocabular Builder intercept (noun) IN tur sept Other Word Forms: intercepted (verb), interception (noun) Definition: An intercept is a point where someone or something is stopped along its wa from one place to another. Main Idea: You can find the intercept(s) of a graph b finding the point(s) where the graph crosses a coordinate ais. Related Words: -intercept; -intercept Use Your Vocabular Choose the correct word from the list to complete each sentence. intercept intercepted interception. During a football game, the home team s quarterback threw an.. The -coordinate of a point where a graph crosses the -ais is a -. A -intercept is the -coordinate of a point where a graph crosses the -ais.. The teacher the message Charlie was passing to his friend. Chapter

18 Ke Concept Slope-Intercept Form of a Linear Equation The slope-intercept form of a linear equation of a nonvertical line is m b. The slope of the line is m. The -intercept is b.. Use the words slope, -intercept, and slope-intercept form to complete the diagram at the right. Problem Writing an Equation in Slope-Intercept Form Got It? What is an equation of the line with slope and -intercept?. Write the numbers and in the correct boes below. m? b?. An equation in slope-intercept form is. Problem Writing an Equation From a Graph Got It? What is an equation of the line shown at the right?. Choose two points on the graph to use to find the slope of the line. What two points will ou use? (, ) and (, ) O. Use the points to find the slope of the line.. The slope of the line is.. Write the slope-intercept form of the equation.. Use the graph to find the -intercept. The -intercept is. Got It? Reasoning If ou use two different points to find the slope of the line, will the equation of the line change? Eplain.. Now choose two points on the line in the above graph that are different from the ones ou chose in Eercise. Use these points to calculate the slope of the line. Lesson -, Part

19 . If ou use two different points to find the slope of the line, will the equation of the line change? Eplain. Problem Writing an Equation From Two Points Got It? What equation in slope-intercept form represents the line that passes through the points (, ) and (, )?. Circle the first step to solve this problem. Underline the second step. Solve for b. Find the slope. Write the slope-intercept form.. Use the points (, ) and (, ) to find the slope of the line. m (). Net, find the -intercept. Substitute the slope for m and the coordinates of one of the points for and. Then solve for b. m? b? b b b. Write the equation of the line in slope-intercept form. Substitute the slope for m and the -intercept for b.? Lesson Check Vocabular Is a linear equation? Eplain.. Does have a slope? Eplain.. Find three points that satisf. (, ) (, ) (, ). Is a linear equation? Eplain. Do ou UNDERSTAND? Chapter

20 - PART Slope-Intercept Form Vocabular Review Underline the true statement in each pair of statements about the graph of the equation.. The graph is a straight line. The graph is a circle.. The slope is. The slope is.. The -intercept is. The -intercept is.. The graph has two -intercepts. The graph has one -intercept. Vocabular Builder model (noun) MAH dul Definition: A model is a representation, eample, or imitation of a thing or person. Man times a model is smaller than the actual item. Math Usage: A mathematical model represents a real-life process or a situation through the use of variables and mathematical operations. Eamples: To stores sell kits that can be put together to be miniature models of actual airplanes, cars, and ships. Henrietta earns $ an hour as a barista in a coffee shop. The equation models how much she makes after working hours. Use Your Vocabular Draw a line from each situation in Column A to its mathematical model in Column B. Column A Column B. Michael mows lawns at a rate of $ an hour.. Tessa has dollars saved and then spends $ at the store.. Georgina walks the same distance each da to work. She walks a total of miles over das. Lesson -, Part

21 Problem Graphing a Linear Equation Got It? What is the graph of?. The ordered pair for the -intercept,, is (, ).. Eplain how ou will use the slope to find another point on the line.. Use the slope,, to find the coordinates. Use the points ou found in Eercises and. of another point on the line. What is the graph of? O Got It? What is the graph of?. The -intercept of the line is, so the point (, ) is on the line.. The coordinates of another point on the line are (, ).. Graph on the grid at the right. Problem Modeling a Function O Got It? A plumber charges a $ fee for a repair plus $ per hour. Write an equation to model the total cost of a repair that takes hours. What graph models the total cost?. Let the number of hours the plumber works. Let the total cost of a repair. When,. So the -intercept is. Chapter

22 . The slope is the amount of change each hour. So, the slope is.. Write an equation to model the cost of a repair.. Complete the table for our equation. Hours () Total Cost (). Graph the data from the table to model the total cost. Be sure to label the aes. O Lesson Check Do ou UNDERSTAND? Writing Describe two different methods ou can use to graph the equation. Which method do ou prefer? Eplain.. Circle two methods ou can use to graph correctl. Use the -intercept to plot Choose two values for Use the -intercept to plot the point (, ). Then use the and find the corresponding the point (, ).Then use the slope of to to plot another -values. Then plot the slope of to plot another point. Then graph the line. points and graph the line. point. Then graph the line.. Which method do ou prefer? Eplain. Math Success Check off the vocabular words that ou understand. linear function -intercept slope-intercept form Rate how well ou can find the slope-intercept form of a linear equation. Need to review Now I get it! Lesson -, Part

23 Name Class Date - Think About a Plan Slope-Intercept Form Hobbies Suppose ou are doing a -piece puzzle. You have alread placed pieces. Ever minute ou place more pieces. a. Write an equation in slope-intercept form to model the number of pieces placed. Graph the equation. b. After more minutes, how man pieces will ou have placed? Understanding the Problem. Is this relationship linear? How do ou know? Planning the Solution. How man pieces have ou alread placed? What does this represent in the slope-intercept form?. What two quantities are used to find the rate of change or slope? What is the slope of this relationship? Getting an Answer. Use our answers in Steps and to write an equation in slope-intercept form to model the number of pieces placed.. Graph the equation on a coordinate grid.. How man pieces will ou have placed after more minutes? Chapter

24 Name Class Date - Practice Form K Slope-Intercept Form Find the slope and -intercept of the graph of each equation Write an equation of a line with the given slope m and -intercept b.. m, b. m, b. m., b. m, b Write an equation in slope-intercept form of each line... O Write an equation in slope-intercept form of the line that passes through the given points.. (, ) and (, ). (, ) and (, ). (, ) and (, ). (, ) and (, ) O Lesson -

25 Name Class Date - Practice (continued) Form K Slope-Intercept Form Graph each equation A car is traveling at mi/h. Write an equation that models the total distance d traveled after h hours. What is the graph of the equation? Chapter

26 Name Class Date - Standardized Test Prep Slope-Intercept Form Multiple Choice For Eercises, choose the correct letter.. What is an equation of the line shown in the graph at the right? A. C. B. D.. What is an equation of the line that has slope and passes through the point (, )? F. G. H. I. O. What is an equation of the line that passes through the points (, ) and (, )? A. B. C. D.. The data shown in the table is linear. Which equation models the data? F. H. G. I.. Karissa earns $ per week plus $ per item she sells. Which equation models the relationship between her pa p per week and the number of items n she sells? A. p n C. n p B. p n D. n p Short Response. What is an equation of the line that passes through (, ) and has slope? What is the graph of the equation? Lesson -

27 - PART Point-Slope Form Vocabular Review. Circle the equation that has a -intercept of.. Circle the equation that is in slope-intercept form. ( ). Circle the statement that is true about the -intercept of an graph. occurs where occurs where occurs where graph on the graph on the graph touches the -ais Vocabular Builder function (noun) FUNGK shun Input Function Rule Related Words: input, output, function rule Definition: A function is a relationship that assigns eactl one output value to each input value. Main Idea: A function is used to describe how one value depends on another. Eample: The function machine above shows that the function assigns an output to ever input according to a specified rule. Use Your Vocabular Complete each sentence with the appropriate word from the list. price sun time. The length of a shadow is a function of the angle of the.. The amount of water that has leaked from a leak faucet is a function of.. The amount of sales ta ou pa is a function of the item s. Output Chapter

28 Ke Concept Point-Slope Form of a Linear Equation The point-slope form of an equation of a nonvertical line with slope m and through point (, ) is m( ).. In the above, what does (, ) represent?. What does m represent? Problem Writing an Equation in Point-Slope Form Got It? A line passes through (, ) and has slope. What is an equation in point-slope form of the line?. Use the point-slope form of an equation. For a line that passes through (, ) and has slope, circle and underline.. Now substitute into point-slope form. m ( ) ( ). An equation of the line is. Problem Graphing Using Point-Slope Form Got It? What is the graph of the equation ( )?. Circle the ordered pair of a point on the graph of ( ). (, ) (, ) (, ) (, ). Circle the correct description of the slope. Go up units and left units Go down units and left units Go up units and right units. Use our answers to Eercises and to graph the line. O Lesson -, Part

29 Lesson Check Do ou know HOW? What is the slope and one point on the graph of ( )?. The point-slope form of the equation of a line is.. The slope of the line is.. The value of is. The value of is.. So one point on the line is (, ). Lesson Check Do ou know HOW? What is the graph of the equation ( )?. Use the point-slope form, m( ), to complete. m. So, the point (, ) is (, ).. How will ou use the slope to find the coordinates of a second point on the line?. Circle the graph of ( ). O O O Chapter

30 - PART Point-Slope Form Vocabular Review. Circle the solution of the equation.. Circle the solution of the equation.. Circle the equation that has a slope of. Vocabular Builder parent function (noun) PEHR unt FUNGK shun parent function f() Related Word: famil of functions Definition: A parent function is the simplest function of a group of functions with common characteristics, called a famil of functions. Eample: For g(), h(), and k(), the parent function is f (). Use Your Vocabular Write the parent function, p(), for each function f (). g() famil of functions h(). f (). f (). f (). f (). f (). f () k() Lesson -, Part

31 Problem Using Two Points to Write an Equation Got It? Use the point (, ) to write an equation of the line shown.. Follow the steps to write the equation of the line shown. Find the slope of the line. Use two points and the slope formula, m =. (, ) O (, ) Use the slope and the point (, ) to write an equation of the line in point-slope form. m( ) ( ) An equation of the line is. Problem Using a Table to Write an Equation Got It? The table shows the number of gallons of water in a tank after hours. The relationship is linear. What is an equation in point-slope form that models the data? What does the slope represent?. Complete the reasoning model below. Think I can use an two points from the table to find the slope. Then I can substitute one point and the slope into the point-slope equation. Finall, I can tell what the slope represents. m Volume of Water in Tank Write Time, (h) m ( ) ( ) The slope represents a rate of?. Water, (gal), Chapter

32 Got It? Reasoning Write the equation from Eercise in slope-intercept form. What does the -intercept represent?. Circle the first step in writing the equation in slope-intercept form. Add to each side. Distribute. Add to each side.. Write the equation in slope-intercept form.. What does the -intercept in our answer to Eercise represent? Lesson Check Do ou UNDERSTAND? Reasoning Can an equation in point-slope form also be written in slope-intercept form? Give an eample to eplain.. Use point-slope form, m( ), and an point and slope to write an equation in point-slope form.. Now write our equation in slope-intercept form.. Can an equation in point-slope form also be written in slope-intercept form? Yes / No Math Success Check off the vocabular words that ou understand. point-slope form Need to review equation Rate how well ou can write equations in point-slope form. Now I get it! Lesson -, Part

33 Name Class Date - Think About a Plan Point-Slope Form Boiling Point The relationship between altitude and the boiling point of water is linear. When the altitude is ft, water boils at. F. When the altitude is ft, water boils at. F. Write an equation giving the boiling point b of water (in degrees Fahrenheit) in terms of the altitude a (in feet). What is the boiling point of water at ft? Understanding the Problem. What are ou given?. In general, how can this information be used to answer the question? Planning the Solution. What is the slope formula?. Substitute given values into the slope formula and simplif. Show our work.. Which point can be used to write the point-slope form of the equation?. What strateg can ou use to solve this problem?. How can ou determine the boiling point of water at ft? Getting an Answer. Write an equation giving the boiling point b of water (in degrees Fahrenheit) in terms of the altitude a.. What is the boiling point of water at ft? Show our work. Chapter

34 Name Class Date - Practice Form K Point-Slope Form Write an equation in point-slope form of the line that passes through the given point and has the given slope.. (, ); m. (, ); m. (, ); m Graph each equation.. ( ). ( ). ( ) Graph the line that passes through the given point and has the given slope m.. (, ); m. (, ); m. (, ); m. Open-Ended Write an equation in each of the following forms that has a slope of. a. point-slope form b. slope-intercept form. Writing Describe what ou know about the graph of a line represented b the equation ( ). Lesson -

35 Name Class Date - Practice (continued) Form K Point-Slope Form Model the data in each table with a linear equation in slope-intercept form. What do the slope and -intercept represent?. Hours Mone. Worked Earned ($)... Time Running (min) Distance (mi) Write an equation in point-slope form of each line... O Write an equation in point-slope form of the line that passes through the given points. Then write the equation in slope-intercept form.. (, ), (, ). (, ), (, ). (, ), (, ). (, ), (, ). Writing Describe how ou would use the point-slope form to write the equation of a line that passes through the points (, ) and (, ) in slope-intercept form.. A restaurant s goal is to serve customers in hours and customers in hours. Write an equation in point-slope form that represents the number of customers served per hour. What is the graph of the equation? O Chapter

36 Name Class Date - Standardized Test Prep Point-Slope Form Multiple Choice For Eercises, choose the correct letter.. Which equation is equivalent to ( )? A. C. B. D.. Which point is located on the line represented b the equation ( )? F. (, ) G. (, ) H. (, ) I. (, ). Which equation represents the line that passes through the points (, )and (, )? A. ( ) C. ( ) B. ( ) D. ( ). Which equation represents the line shown in the graph? F. G. H. ( ) I. ( ). The population of a cit increases b people each ear. In, the population is projected to be, people. What is an equation that gives the cit s population p (in thousands of people) ears after? A. p C. p ( ) B. p ( ) D. p Short Response. The table shows the cost of a large cheese pizza with additional toppings on it. a. What is an equation in point-slope form that represents the relationship between the number of toppings and the cost of the pizza? b. What is the graph of the equation? O Toppings Cost ($)... Lesson -

37 - Standard Form Vocabular Review Underline the correct word to complete each sentence.. Line z is a horizontal / vertical line.. Line p is a horizontal / vertical line. z. A line with a slope of is horizontal / vertical. p. A line with an undefined slope is horizontal / vertical. Vocabular Builder standard (adjective) STAN durd Other Word Forms: standards (plural noun), standardized (adjective) Main Idea: Something that is standard is well known and widel used. Eample: The standard measure of weight used in the U.S. is the pound. Math Usage: The standard form of a linear equation is A B C, where A, B, and C are real numbers, and A and B are not both zero. Opposites: different, irregular Use Your Vocabular Underline the correct word(s) to complete each sentence.. In gmnastics, judges use a set of standards / standardized to award a score.. Most English words have a standard / standardized pronunciation.. Man states use standard / standardized tests to assess their students performance.. Multiple Choice Which linear equation is in standard form? ( ) Chapter

38 Problem Finding - and -Intercepts Got It? What are the - and -intercepts of the graph of? Complete each sentence.. To find the -intercept, let.. To find the -intercept, let.. Find the -intercept.. Find the -intercept.?? Got It? What are the - and -intercepts of the graph of?. Find the -intercept.. Find the -intercept.?? Problem Graphing a Line Using Intercepts Got It? What is the graph of?. Circle the -intercept of.. Circle the -intercept of.. Use the intercepts to graph the line. O Lesson -

39 Problem Graphing Horizontal and Vertical Lines Got It? What is the graph of the equation?. The equation means that for all values of, the value of is.. For the reason given above, the graph of is a horizontal / vertical line.. Graph the equation. O Problem Transforming to Standard Form Got It? Write ( ) in standard form using integers.. Circle the first step to put ( ) in standard form. Solve for. Multipl both sides b. Add to both sides.. Now find the standard form of the equation using integers.. The standard form of the equation is??. Problem Using Standard Form as a Model Got It? A media download store sells songs for $ each and movies for $ each. You have $ to spend. Write and graph an equation that describes the numbers of songs and movies ou can purchase for $.. You cannot bu a fraction of a song or movie. Describe how ou will use the graph of the equation to find solutions that make sense. Chapter

40 Number of Movies. Use the model to help ou complete the equation. Relate cost of a song number of songs cost of a movie number of movies is $ Define Let the number of songs purchased. Let. Write. Find the intercepts of the equation.. Use the intercepts to graph the equation. O Number of Songs Lesson Check Do ou UNDERSTAND? Vocabular Tell whether each linear equation is in slope-intercept form, point-slope form, or standard form. ( ) ( ). Draw a line from each equation in Column A to the form of the equation in Column B. Column A ( ) ( ) Math Success Check off the vocabular words that ou understand. linear equation -intercept standard form Rate how well ou can graph a linear equation using intercepts. Need to review Column B m b (Slope-Intercept Form) m( ) (Point-Slope Form) A B C (Standard Form) Now I get it! Lesson -

41 Name Class Date - Think About a Plan Standard Form Sports A football team scores points. All of the points come from field goals worth points and touchdowns (with successful etra-point attempts) worth points. Write and graph a linear equation that represents this situation. List ever possible combination of field goals and touchdowns the team could have scored. Understanding the Problem. What are ou given?. How can touchdowns and field goals be represented? How can these be written as terms to represent the point value of each? Planning the Solution. What is the equation in standard form that models the situation?. How can ou find the -intercept?. How can ou find the -intercept?. How can ou use the intercepts to graph the line? Getting an Answer. Graph the relation on a coordinate grid.. Use the graph to determine and list all of the combinations. Chapter

42 Name Class Date - Practice Form K Standard Form Find the - and -intercepts of the graph of each equation..... Draw a line with the given intercepts.. -intercept:. -intercept: -intercept: -intercept: Graph each equation using - and -intercepts For each equation, tell whether its graph is a horizontal or a vertical line... Graph each equation... Lesson -

43 Name Class Date - Practice (continued) Form K Standard Form. Writing Eplain how ( ) can be rewritten into standard form. Then show our work in transforming the equation to standard form. Write each equation in standard form using integers... ( ). ( ).. You work two jobs. At the first job, ou earn $ per hour. At the second job, ou earn $ per hour. You earned $ last week. Write and graph an equation that represents this situation. What are three combinations of hours ou could have worked at each job?. Mike was the kicker for the football team. He scored points during the season kicking field goals ( points) and etra points ( point). Write and graph an equation that represents this situation. What are three combinations of field goals and etra points he could have made? For each graph, find the - and -intercepts. Then write an equation in standard form using integers... O Find the - and -intercepts of the line that passes through the given points.. (, ), (, ). (, ), (, ) O Chapter

44 Name Class Date - Standardized Test Prep Standard Form Multiple Choice For Eercises, choose the correct letter.. What is written in standard form using integers? A. B. C. D.. Which of the following is an equation of a vertical line? F. G. H. I.. What are the - and -intercepts of the graph of A. -intercept: C. -intercept: -intercept: -intercept:. B. -intercept: D. -intercept: -intercept: -intercept:.. Cherl is planning to spend $ on a Christmas gift for her father. He needs new socks and ties. A store has socks s and ties t on sale for $ and $, respectivel. Which equation models this situation? F. s t H. s t G. s t I. t s Etended Response. The grocer store is selling eggs for $ per dozen and bacon for $ per pound. You plan to spend $ in food for the benefit breakfast. Write and graph an equation that represents this situation. What are three combinations of dozens of eggs and pounds of bacon ou can purchase? Lesson -

45 - Parallel and Perpendicular Lines Vocabular Review. Circle the product of a number and its reciprocal.. Circle the pairs of numbers that are reciprocals. and Vocabular Builder and and and parallel (adjective) PA ruh lel Related Word: perpendicular (adjective) Math Usage: Lines that are parallel are lines in the same plane that never intersect. Using smbols: * AB ) * CD ) means line AB is parallel to line CD. Eample: The stripes on the American flag are parallel. Use Your Vocabular Picture A Picture B Picture C Complete each sentence with parallel or perpendicular.. The railroad tracks in Picture A are.. The window bars in Picture B that do NOT meet are.. The roads in Picture C are. Chapter

46 Ke Concept Slopes of Parallel Lines Nonvertical lines are parallel if the have the same slope and different -intercepts. Vertical lines are parallel if the have different -intercepts.. Draw a line from each equation in Column A to an equation whose graph is parallel in Column B. Column A Column B O Problem Writing an Equation of a Parallel Line Got It? A line passes through (, ) and is parallel to the graph of. What equation represents the line in slope-intercept form?. The slope of the graph of is.. The slope of an line parallel to the graph of is.. Use point-slope form to find an equation of the line that passes through (, ) and uses the slope from Eercise. m( ) Ke Concept Slopes of Perpendicular Lines Two nonvertical lines are perpendicular if the product of their slopes is. Two numbers whose product is are called opposite reciprocals. A vertical line and a horizontal line are also perpendicular.. Multiple Choice The slope of a line is. What is the slope of a line perpendicular to that line? O Lesson -

47 Problem Classifing Lines Got It? Are the graphs of the equations and parallel, perpendicular, or neither? Eplain.. Write the equation in slope-intercept form.. The slope of the line is.. The slope of the line is.. Are the lines parallel, perpendicular, or neither? Eplain. Problem Writing an Equation of a Perpendicular Line Got It? A line passes through (, ) and is perpendicular to the graph of. What equation represents the line in slope-intercept form?. Find the slope of the perpendicular line. Slope of the given line opposite reciprocal (slope of perpendicular line). The slope of the perpendicular line is.. Use point-slope form and the point (, ) to write an equation of the perpendicular line. m? ( ) Chapter

48 Problem Solving a Real-World Problem Got It? An architect uses software to design a ceiling. The architect needs to enter an equation that represents a new beam. The new beam will be parallel to the eisting beam, which is shown b the red line. The new beam will pass through the corner at (, ). What is an equation in slope-intercept form that represents the new beam?. Use the slope formula to find the slope of the red line that represents the eisting beam. m O Eisting beam CEILING VIEW. In order for the new beam to be parallel to the eisting beam, their slopes should be the same / opposite reciprocals.. Now find the equation of the line that will be parallel to the eisting line and will pass through (, ). Lesson Check Do ou UNDERSTAND? Compare and Contrast How is determining if two lines are parallel similar to determining if the are perpendicular? How are the processes different?. To determine if two lines are parallel,. To determine if two lines are perpendicular, what do ou need to do? what do ou need to do?. How are the processes similar?. How are the processes different? Math Success Check off the vocabular words that ou understand. parallel lines perpendicular lines opposite reciprocals Rate how well ou can write equations of parallel and perpendicular lines. Need to review Now I get it! Lesson -

49 Name Class Date - Think About a Plan Parallel and Perpendicular Lines Agriculture Two farmers use combines to harvest corn from their fields. One farmer has acres of corn, and the other has acres of corn. Each farmer s combine can harvest acres per da. Write two equations for the number of acres of corn not harvested after das. Are the graphs of the equations parallel, perpendicular, or neither? How do ou know? Understanding the Problem. What is the difference between the two farms? What is the same?. How can ou determine if the graphs of two equations are parallel, perpendicular, or neither? Planning the Solution. What is an algebraic epression that represents the amount of corn each farmer can harvest per da?. Write an equation representing the number of acres of corn not harvested after das on the farm with acres.. Write an equation representing the number of acres of corn not harvested after das on the farm with acres. Getting an Answer. Write the equations in Steps and in slope-intercept form.. What are the slopes of the equations?. Are the graphs of the equations parallel, perpendicular, or neither? Eplain. Chapter

50 Name Class Date - Practice Form K Parallel and Perpendicular Lines Write an equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of the given equation.. (, );. (, );. (, );. (, ); Determine whether the graphs of the given equations are parallel, perpendicular, or neither. Eplain..... Determine whether each statement is alwas, sometimes, or never true. Eplain.. Two lines with different slopes are parallel.. Two lines with the same -intercept are perpendicular.. Two lines whose slopes are opposites of each other are perpendicular. Lesson -

51 Name Class Date - Practice (continued) Form K Parallel and Perpendicular Lines Write an equation of the line that passes through the given point and is perpendicular to the graph of the given equation.. (, );. (, );. (, );. (, );. Open-Ended Write the equations of three lines whose graphs are parallel to.. Open-Ended Write the equations of two lines whose graphs are perpendicular to.. What is the slope of a line that is parallel to?. What is the slope of a line that is perpendicular to?. What is the slope of a line that is parallel to?. What is the slope of a line that is perpendicular to?. On a map, Center St. passes through coordinates (, ) and (, ). Merrie Rd. intersects Center St. and passes through coordinates (, ) and (, ). Are these streets perpendicular? Eplain. Chapter

52 Name Class Date - Standardized Test Prep Parallel and Perpendicular Lines Multiple Choice For Eercises, choose the correct letter.. Which equation has a graph parallel to the graph of? A. B. C. D.. Which equation has a graph perpendicular to the graph of? F. G. H. I.. Which equation is the equation of a line that passes through (, ) and is perpendicular to? A. B. C. D. * ). Which of the following coordinates for P will make MN parallel to OP in the diagram at the right? F. (, ) H. (, ) G. (, ) I. (, ). Segment XY represents the path of an airplane that passes through the coordinates (, ) and (, ). What is the slope of a line that represents the path of another airplane that is traveling parallel to the first airplane? A. C. B. Short Response D. N(, ) O(, ) O. A cit designer is drawing the road map for a new housing development. Palm St. runs through the coordinates (, ) and (, ) on the map. Pepperdine St. is going to run perpendicular to Palm St. The coordinates of Pepperdine St. are (, ) and (, ). What is the value of? What is the equation for the line representing Pepperdine St. in slope-intercept form? M(, ) Lesson -

53 - Scatter Plots and Trend Lines Vocabular Review A scatter plot is a graph that relates two sets of data. Plot each ordered pair on the graph at the right to make a scatter plot.. (, ). (, ). (, ). (, ) O Vocabular Builder correlation (noun) kawr uh LAY shun Related Words: correlate (verb), relationship (noun), relate (verb), scatter plot (noun) Definition: A correlation is a measure of the strength of a relationship between two quantities. Eample: The more a student studies, the higher the student s grades tend to be. So, there is a correlation between time spent studing and grades. Use Your Vocabular Label each scatter plot positive correlation, negative correlation, or no correlation.... increases as increases decreases as increases and are not related Chapter

54 Problem Making a Scatter Plot and Describing Its Correlation Got It? Make a scatter plot of the data in the table. What tpe of relationship does the scatter plot show? Dollars Spent Gallons Bought Gasoline Purchases Let dollars spent. Let.. Use the data to make a scatter plot.. Underline the correct word or words to complete each sentence. The number of gallons bought tends to increase / decrease as the number of dollars spent increases / decreases. The two sets of data have a positive / negative correlation O Dollars Spent Got It? Reasoning Consider the population of a cit and the number of letters in the name of the cit. Would ou epect a positive correlation, a negative correlation, or no correlation between the two sets of data? Eplain our reasoning.. As an eample, think of the cit or town that ou live in. How man letters are in the name of our cit and approimatel how man people live there?. Now think of another cit of a ver different size than the one ou chose for Eercise. How man letters are in the name of this cit and approimatel how man people live there?. Is the size of either cit dependent on the number of letters in its name? Yes / No. What kind of correlation would ou epect between the two sets of data? Eplain. A trend line is a line on a scatter plot, drawn near the points, that shows a correlation. There should be about the same number of points above the line as below it. Lesson -

55 Problem Writing an Equation of a Trend Line Got It? Make a scatter plot of the data. Draw a trend line and write its equation. What is the approimate bod length of a -month-old panda? Age (month) Bod Length (in.). Bod Length of a Panda Make a scatter plot and draw a trend line.. Write the equation of the trend line that ou drew. O Age (month) Bod Length (in.). Use the equation of our trend line to estimate the bod length of a -month-old panda.. A -month-old panda would be approimatel inches in length. Problem Finding the Line of Best Fit Got It? For data of tuition and fees charged at public four-ear colleges, the equation of the line of best fit is.,., where the ear at the beginning of the academic ear and cost. Predict the cost of attending a public four-ear college in the academic ear.. Let.. Complete the steps to find the estimated cost..?,.,. <. The cost of attending a public four-ear college in the academic ear will be about $. Causation is when a change in one quantit causes a change in a second quantit. A correlation between quantities does not alwas impl causation. Chapter

56 Problem Identifing Whether Relationships Are Causal Got It? Consider the cost of a famil's vacation and the size of their house. Is there likel to be a correlation? If so, does the correlation reflect a causal relationship? Eplain.. Is there likel to be a correlation between the cost of a famil s vacation and the size of their house? Eplain.. If there is a correlation, does the correlation reflect a causal relationship? Eplain. Lesson Check Do ou UNDERSTAND? Error Analsis Refer to the table below. A student sas that the data have a negative correlation because as decreases, also decreases. What is the student s error? Math Success Need to review. Make a scatter plot of the data.. The scatter plot shows a positive / negative correlation.. Eplain the student s error. Check off the vocabular words that ou understand. Now I get it! O scatter plot correlation trend line causation Rate how well ou can make a scatter plot and determine the tpe of correlation. Lesson -

57 Name Class Date - Think About a Plan Scatter Plots and Trend Lines U.S. Population Use the data below. Year Male,,,,,,, Female,,,,,,, SOURCE: U.S. Census Bureau. Estimated Population of the United States (thousands) a. Make a scatter plot of the data pairs (male population, female population). b. Draw a trend line and write its equation. c. Use our equation to predict the U.S. female population if the U.S. male population increases to,,. d. Reasoning Consider a scatter plot of the data pairs (ear, male population). Would it be reasonable to use this scatter plot to predict the U.S. male population in? Eplain our reasoning.. Make a scatter plot of the data pairs using the male population for the -coordinates and the female population for the -coordinates for each ear.. Draw the trend line onto the scatter plot.. How do ou determine the equation of a trend line? What is the equation of this trend line? Show our work.. Substitute,, for to predict the female population.. Make a scatter plot of the data pairs (ear, male population).. Would it be reasonable to use this scatter plot to predict the U.S. male population in? Eplain our reasoning. Chapter