Name Date Chapter Fair Game Review Evaluate the epression when = and =.... 0 +. 8( ) Evaluate the epression when a = 9 and b =.. ab. a ( b + ) 7. b b 7 8. 7b + ( ab ) 9. You go to the movies with five friends. You and one of our friends each bu a ticket and a bag of popcorn. The rest of our friends bu just one ticket each. + + represents the situation. Evaluate the epression The epression ( ) when tickets cost $7. and a bag of popcorn costs $.. Copright Big Ideas Learning, LLC 7
Name Date Chapter Fair Game Review (continued) Use the graph to answer the question. 0. Write the ordered pair that corresponds to Point D. F A G. Write the ordered pair that corresponds to Point H. D O. Which point is located at (, )? E C H B. Which point is located at ( 0, )?. Which point(s) are located in Quadrant IV?. Which point(s) are located in Quadrant III? Plot the point.. (, ) 7. ( 0, ) O 8. (, ) 9. (, 0) 0. (, ) 8 Copright Big Ideas Learning, LLC
Name Date. Graphing Linear Equations For use with Activit. Essential Question How can ou recognize a linear equation? How can ou draw its graph? ACTIVITY: Graphing a Linear Equation Work with a partner. a. Use the equation = + to complete the table. (Choose an two -values and find the -values). b. Write the two ordered pairs given b the table. These are called solution points of the equation. = + Solution Points c. PRECISION Plot the two solution points. Draw a line eactl through the two points. d. Find a different point on the line. Check that this point is a solution point of the equation = +. O e. LOGIC Do ou think it is true that an point on the line is a solution point of the equation = +? Eplain. Copright Big Ideas Learning, LLC 9
Name Date. Graphing Linear Equations (continued) f. Choose five additional -values for the table. (Choose positive and negative -values.) Plot the five corresponding solution points on the previous page. Does each point lie on the line? Solution Points = + g. LOGIC Do ou think it is true that an solution point of the equation = + is a point on the line? Eplain. h. Wh do ou think = a + b is called a linear equation? ACTIVITY: Using a Graphing Calculator Use a graphing calculator to graph = +. a. Enter the equation = + into our calculator. b. Check the settings of the viewing window. The boundaries of the graph are set b the minimum and maimum - and -values. The numbers of units between the tick marks are set b the - and -scales. This is the standard viewing window. 70 Copright Big Ideas Learning, LLC
Name Date. Graphing Linear Equations (continued) c. Graph = + on our calculator. d. Change the settings of the viewing window to match those shown. Compare the two graphs. 0 0 0 = + 0 8 = + What Is Your Answer?. IN YOUR OWN WORDS How can ou recognize a linear equation? How can ou draw its graph? Write an equation that is linear. Write an equation that is not linear.. Use a graphing calculator to graph = in the standard viewing window. a. Can ou tell where the line crosses the -ais? Can ou tell where the line crosses the -ais? b. How can ou adjust the viewing window so that ou can determine where the line crosses the - and -aes?. CHOOSE TOOLS You want to graph =..8. Would ou graph it b hand or b using a graphing calculator? Wh? Copright Big Ideas Learning, LLC 7
Name Date. Practice For use after Lesson. Graph the linear equation. Use a graphing calculator to check our graph, if possible.. =. = O O Solve for. Then graph the equation. Use a graphing calculator to check our graph.. + =. = O O. The equation = + represents the cost (in dollars) of renting a movie after das of late charges. a. Graph the equation. O b. Use the graph to determine how much it costs after das of late charges. 7 Copright Big Ideas Learning, LLC
Name Date. Slope of a Line For use with Activit. Essential Question How can the slope of a line be used to describe the line? Slope is the rate of change between an two points on a line. It is the measure of the steepness of the line. To find the slope of a line, find the ratio of the change in (vertical change) to the change in (horizontal change). slope = change in change in 7 Slope = 7 ACTIVITY: Finding the Slope of a Line Work with a partner. Find the slope of each line using two methods. Method : Use the two black points. Method : Use the two gra points. Do ou get the same slope using each method? Wh do ou think this happens? a. b. c. d. Copright Big Ideas Learning, LLC 7
Name Date. Slope of a Line (continued) ACTIVITY: Using Similar Triangles Work with a partner. Use the figure shown. a. ΔABC is a right triangle formed b drawing a horizontal line segment from point A and a vertical line segment from point B. Use this method to draw another right triangle, Δ DEF. 0 9 8 7 A(, ) E(, 0) D(9, ) B(, ) C(, ) 7 8 9 0 b. What can ou conclude about Δ ABC and Δ DEF? Justif our conclusion. c. For each triangle, find the ratio of the length of the vertical side to the length of the horizontal side. What do these ratios represent? d. What can ou conclude about the slope between an two points on the line? ACTIVITY: Drawing Lines with Given Slopes Work with a partner. a. Draw two lines with slope. One line and the other line passes through (, ), passes through (, 0 ). What do ou notice about the two lines? 7 Copright Big Ideas Learning, LLC
Name Date. Slope of a Line (continued) b. Draw two lines with slope. One line,, and the other line passes through ( ) passes through (, ). What do ou notice about the two lines? c. CONJECTURE Make a conjecture about two different nonvertical lines in the same plane that have the same slope. d. Graph one line from part (a) and one line from part (b) in the same coordinate plane. Describe the angle formed b the two lines. What do ou notice about the product of the slopes of the two lines? e. REPEATED REASONING Repeat part (d) for the two lines ou did not choose. Based on our results, make a conjecture about two lines in the same plane whose slopes have a product of. What Is Your Answer?. IN YOUR OWN WORDS How can ou use the slope of a line to describe the line? Copright Big Ideas Learning, LLC 7
Name Date Practice. For use after Lesson. Find the slope of the line... 9 (, ) (, 9) O 9 (, ) (, ) (, ). (, ) O. (, ) (, ). Which set of stairs is more difficult to climb? Eplain. 0 in. in. in. 8 in. Staircase 7 Staircase Copright Big Ideas Learning, LLC
Name Date Etension. Practice For use after Etension. Which lines are parallel? How do ou know?.. R (, ) (, ) (, ) G B (, ) (0, ) (, ) (, ) B (, ) R (, ) (, ) (, ) G (, ) Are the given lines parallel? Eplain our reasoning.. =, =. =, =. Is the quadrilateral a parallelogram? Justif our answer. A B D C Copright Big Ideas Learning, LLC 77
Name Date Etension. Practice (continued) Which lines are perpendicular? How do ou know? (, ) B R (, ) (, ) (, 0) G B (, ) (, ) G (, ) (, ). 7. R (, ) (, ) (, ) (, ) Are the given lines perpendicular? Eplain our reasoning. 8. = 0, = 9. =, = 0. Is the parallelogram a rectangle? Justif our answer. K L J M 78 Copright Big Ideas Learning, LLC
Name Date. Graphing Proportional Relationships For use with Activit. Essential Question How can ou describe the graph of the equation = m? ACTIVITY: Identifing Proportional Relationships Work with a partner. Tell whether and are in a proportional relationship. Eplain our reasoning. a. Mone b. Helicopter Earnings (dollars) 70 0 0 0 0 0 0 0 0 7 Hours worked Height (meters) 0 0 0 0 0 7 Time (seconds) c. Tickets d. Pizzas Cost (dollars) 0 0 00 80 0 0 0 0 0 7 Number of tickets Cost (dollars) 0 0 0 0 0 7 Number of pizzas e. f. Laps, Time (seconds), 90 00 80 Cups of Sugar, Cups of Flour, Copright Big Ideas Learning, LLC 79
Name Date. Graphing Proportional Relationships (continued) ACTIVITY: Analzing Proportional Relationships Work with a partner. Use onl the proportional relationships in Activit to do the following. Find the slope of the line. Find the value of for the ordered pair (, ). What do ou notice? What does the value of represent? ACTIVITY: Deriving an Equation Work with a partner. Let (, ) represent an point on the graph of a proportional relationship. (, ) (, m) a. Eplain wh the two triangles are similar. (0, 0) b. Because the triangles are similar, the corresponding side lengths are proportional. Use the vertical and horizontal side lengths to complete the steps below. m = Ratios of side lengths = m Simplif. = m Multiplication Propert of Equalit What does the final equation represent? 80 Copright Big Ideas Learning, LLC
Name Date. Graphing Proportional Relationships (continued) c. Use our result in part (b) to write an equation that represents each proportional relationship in Activit. What Is Your Answer?. IN YOUR OWN WORDS How can ou describe the graph of the equation m? = How does the value of m affect the graph of the equation?. Give a real-life eample of two quantities that are in a proportional relationship. Write an equation that represents the relationship and sketch its graph. Copright Big Ideas Learning, LLC 8
Name Date. Practice For use after Lesson.. The amount p (in dollars) that ou earn b working h hours is represented b the equation p = 9. h Graph the equation and interpret the slope. 90 80 70 0 0 0 0 0 0 0 0 7 8 9. The cost c (in dollars) to rent a biccle is proportional to the number h of hours that ou rent the biccle. It costs $0 to rent the biccle for hours. a. Write an equation that represents the situation. b. Interpret the slope. c. How much does it cost to rent the biccle for hours? 8 Copright Big Ideas Learning, LLC
Name Date. Graphing Linear Equations in Slope-Intercept Form For use with Activit. Essential Question How can ou describe the graph of the equation = m + b? ACTIVITY: Analzing Graphs of Lines Work with a partner. Graph each equation. Find the slope of each line. Find the point where each line crosses the -ais. Complete the table. Equation Slope of Graph Point of Intersection with -ais a. = + b. = + c. = d. = + e. = + f. = g. h. = = i. = + Copright Big Ideas Learning, LLC 8
Name Date. Graphing Linear Equations in Slope-Intercept Form (continued) Equation Slope of Graph Point of Intersection with -ais j. = k. Do ou notice an relationship between the slope of the graph and its equation? Between the point of intersection with the -ais and its equation? Compare the results with those of other students in our class. ACTIVITY: Deriving an Equation Work with a partner. a. Look at the graph of each equation in Activit. Do an of the graphs represent a proportional relationship? Eplain. b. For a nonproportional linear relationship, the graph crosses 0, b, where b does not equal 0. the -ais at some point ( ) Let (, ) represent an other point on the graph. You can use the formula for slope to write the equation for a nonproportional linear relationship. Use the graph to complete the steps. = m Slope formula (0, b) (, ) = m Substitute values. = m Simplif. = m Multiplication Propert of Equalit = m Simplif. = m + Addition Propert of Equalit 8 Copright Big Ideas Learning, LLC
Name Date. Graphing Linear Equations in Slope-Intercept Form (continued) c. What do m and b represent in the equation? What Is Your Answer?. IN YOUR OWN WORDS How can ou describe the graph of the equation = m + b? a. How does the value of m affect the graph of the equation? b. How does the value of b affect the graph of the equation? c. Check our answers to parts (a) and (b) with three equations that are not in Activit.. LOGIC Wh do ou think = + m b is called the slope-intercept form of the equation of a line? Use drawings or diagrams to support our answer. Copright Big Ideas Learning, LLC 8
Name Date. Practice For use after Lesson. Find the slope and -intercept of the graph of the linear equation.. = + 9. =. + = 8 Graph the linear equation. Identif the -intercept. Use a graphing calculator to check our answer.. = +. 0 = O O. The equation = 90 + 0 represents the time (in minutes) left after games of a tournament. a. Graph the equation. b. Interpret the -intercept and slope. 8 Copright Big Ideas Learning, LLC
Name Date. Graphing Linear Equations in Standard Form For use with Activit. Essential Question How can ou describe the graph of the equation a + b = c? ACTIVITY: Using a Table to Plot Points Work with a partner. You sold a total of $ worth of tickets to a school concert. You lost track of how man of each tpe of ticket ou sold. adult Number of Number of + = adult tickets student student tickets a. Let represent the number of adult tickets. Let represent the number of student tickets. Write an equation that relates and. b. Complete the table showing the different combinations of tickets ou might have sold. Number of Adult Tickets, Number of Student Tickets, c. Plot the points from the table. Describe the pattern formed b the points. 9 8 7 d. If ou remember how man adult tickets ou sold, can ou determine how man student tickets ou sold? Eplain our reasoning. 0 0 7 8 9 Copright Big Ideas Learning, LLC 87
Name Date. Graphing Linear Equations in Standard Form (continued) ACTIVITY: Rewriting an Equation Work with a partner. You sold a total of $ worth of cheese. You forgot how man pounds of each tpe of cheese ou sold. lb Pounds of swiss + Pound of cheddar lb = a. Let represent the number of pounds of swiss cheese. Let represent the number of pounds of cheddar cheese. Write an equation that relates and. b. Rewrite the equation in slope-intercept form. Then graph the equation. 9 8 7 0 88 0 7 8 9 Copright Big Ideas Learning, LLC
Name Date. Graphing Linear Equations in Standard Form (continued) c. You sold pounds of cheddar cheese. How man pounds of swiss cheese did ou sell? d. Does the value =. make sense in the contet of the problem? Eplain. What Is Your Answer?. IN YOUR OWN WORDS How can ou describe the graph of the equation a + b = c?. Activities and show two different methods for graphing a + b = c. Describe the two methods. Which method do ou prefer? Eplain.. Write a real-life problem that is similar to those shown in Activities and.. Wh do ou think it might be easier to graph + = 0 without rewriting it in slope-intercept form and then graphing? Copright Big Ideas Learning, LLC 89
Name Date. Practice For use after Lesson. Write the linear equation in slope-intercept form.. = 7. + =. = 0 7 Graph the linear equation using intercepts. Use a graphing calculator to check our graph.. =. + 9 = 7 O O. You go shopping and bu shirts for $ and jeans for $8. The total spent is $8. a. Write an equation in standard form that models how much mone ou spent. b. Graph the equation and interpret the intercepts. O 90 Copright Big Ideas Learning, LLC
Name Date. Writing Equations in Slope-Intercept Form For use with Activit. Essential Question How can ou write an equation of a line when ou are given the slope and -intercept of the line? ACTIVITY: Writing Equations of Lines Work with a partner. Find the slope of each line. Find the -intercept of each line. Write an equation for each line. What do the three lines have in common? a. b. 7 c. d. 8 7 Copright Big Ideas Learning, LLC 9
Name Date. Writing Equations in Slope-Intercept Form (continued) ACTIVITY: Describing a Parallelogram Work with a partner. Find the area of each parallelogram. Write an equation that represents each side of each parallelogram. a. b. 7 ACTIVITY: Interpreting the Slope and the -Intercept Work with a partner. The graph shows a trip taken b a car, where t is the time (in hours) and is the distance (in miles) from Phoeni. a. Find the -intercept of the graph. What does it represent? Distance (miles) 00 00 00 00 Car Trip 00 0 0 8 0 t Time (hours) 9 Copright Big Ideas Learning, LLC
Name Date. Writing Equations in Slope-Intercept Form (continued) b. Find the slope of the graph. What does it represent? c. How long did the trip last? d. How far from Phoeni was the car at the end of the trip? e. Write an equation that represents the graph. What Is Your Answer?. IN YOUR OWN WORDS How can ou write an equation of a line when ou are given the slope and the -intercept of the line? Give an eample that is different from those in Activities,, and.. Two sides of a parallelogram are represented b the equations = + and = +. Give two equations that can represent the other two sides. Copright Big Ideas Learning, LLC 9
Name Date. Practice For use after Lesson. Write an equation of the line in slope-intercept form... 0 (, 9) 8 (0, 7) 8 (, 7) O O (, 8). (, ). 8 0 (, 9) 8 0 (, ) (, 8) Write an equation of the line that passes through the points.. (, 8 ), (, 8). (, ), (, ) 7. (, 0 ), (, 0) 8. You organize a garage sale. You have $0 at the beginning of the sale. You earn an average of $0 per hour. Write an equation that represents the amount of mone ou have after hours. 9 Copright Big Ideas Learning, LLC
Name Date.7 Writing Equations in Point-Slope Form For use with Activit.7 Essential Question How can ou write an equation of a line when ou are given the slope and a point on the line? ACTIVITY: Writing Equations of Lines Work with a partner. Sketch the line that has the given slope and passes through the given point. Find the -intercept of the line. Write an equation of the line. a. m = b. m = 8 7 7 c. m = d. m = 7 7 Copright Big Ideas Learning, LLC 9
Name Date.7 Writing Equations in Point-Slope Form (continued) ACTIVITY: Deriving an Equation Work with a partner. a. Draw a nonvertical line that passes,. through the point ( ) b. Plot another point on our line. Label,. This point this point as ( ) represents an other point on the line. O (, ) c. Label the rise and run of the line,,. through the points ( ) and ( ) d. The rise can be written as. The run can be written as. Eplain wh this is true. e. Write an equation for the slope m of the line using the epressions from part (d). f. Multipl each side of the equation b the epression in the denominator. Write our result. What does this result represent? 9 Copright Big Ideas Learning, LLC
Name Date.7 Writing Equations in Point-Slope Form (continued) ACTIVITY: Writing an Equation Work with a partner. For months, ou saved $ a month. You now have $7 in our savings account. Draw a graph that shows the balance in our account after t months. Use our result from Activit to write an equation that represents the balance A after t months. Balance (dollars) Savings Account A 0 00 7 0 00 7 0 0 0 7 8 9 t Time (months) What Is Your Answer?. Redo Activit using the equation ou found in Activit. Compare the results. What do ou notice?. Wh do ou think m( ) = is called the point-slope form of the equation of a line? Wh do ou think this is important?. IN YOUR OWN WORDS How can ou write an equation of a line when ou are given the slope and a point on the line? Give an eample that is different from those in Activit. Copright Big Ideas Learning, LLC 97
Name Date.7 Practice For use after Lesson.7 Write in point-slope form an equation of the line that passes through the given point that has the given slope. ;,. m = ; (, ). m = ( ) Write in slope-intercept form an equation of the line that passes through the given points.. (, 0 ), (, ). (, 0 ), (, 0). The total cost for bowling includes the fee for shoe rental plus a fee per game. The cost of each game increases the price b $. After games, the total cost with shoe rental is $. a. Write an equation to represent the total cost to rent shoes and bowl games. b. How much is shoe rental? How is this represented in the equation? 98 Copright Big Ideas Learning, LLC