Contents Introduction to Kestone Algebra I... Module Operations and Linear Equations & Inequalities...9 Unit : Operations with Real Numbers and Epressions, Part...9 Lesson Comparing Real Numbers A... Lesson Simplifing Square Roots A... Lesson Greatest Common Factor and Least Common Multiple A... 6 Lesson Eponents, Roots, and Absolute Value A...9 Lesson Simplifing Epressions A... Unit Constructed-Response Review...7 Unit : Operations with Real Numbers and Epressions, Part... Lesson Estimation A...6 Lesson Polnomial Epressions A... Lesson Factoring Algebraic Epressions A... Lesson Factoring Trinomial Epressions A...7 Lesson Simplifing Rational Epressions A... Unit Constructed-Response Review... Unit : Linear Equations...6 Lesson Linear Equations, Part A..., A...6 Lesson Linear Equations, Part A..., A..., A...67 Lesson Sstems of Linear Equations A..., A...7 Unit Constructed-Response Review...8 Unit : Linear Inequalities...89 Lesson Linear Inequalities A..., A...9 Lesson Compound Inequalities A..., A...9 Lesson Sstems of Linear Inequalities A..., A...99 Unit Constructed-Response Review...8
Module Linear Functions and Data Organizations... Unit : Functions... Lesson Identifing and Representing Patterns A...6 Lesson Relations and Functions A..., A... Lesson Linear Functions A..., A...7 Unit Constructed-Response Review... Unit 6: Coordinate Geometr... Lesson Slope, Intercepts, and Rates of Change A..., A..., A... Lesson Writing Linear Equations A..., A... Lesson Equations of Lines of Best Fit A...8 Unit 6 Constructed-Response Review...6 Unit 7: Data Analsis...7 Lesson Central Tendenc and Dispersion A..., A...7 Lesson Predictions from Data A...79 Lesson Representations of Data A...8 Lesson Predictions from Scatter Plots A...9 Lesson Probabilit of Compound Events A...9 Unit 7 Constructed-Response Review...98 Glossar...7 Formula Sheet...
LESSON Slope, Intercepts, and Rates of Change A..., A..., A... Slope Slope is a measure of the steepness of a line. It describes a rate of change. The slope of a line can be found using either of these methods:. On the graph of a line, determine the vertical change (the rise ) over the horizontal change (the run ) from one point to another. vertical change slope horizontal change rise run run rise,,. Use the slope formula. For an two points on a line, _, + and _, + and, slope. A line that slants upward from left to right alwas has a positive slope. A line that slants downward from left to right alwas has a negative slope. It is a good idea to check the slope of a line found when looking at a graph using rise over run b also using the slope formula. Horizontal lines have a slope of. Vertical lines have an undefined slope. Tr this sample question. S- What is the slope of the line graphed below? 6 6 8 A B C D Unit 6 Coordinate Geometr
Find the slope using the rise over the run, rise or run. B looking at the graph, ou can see that the line has a rise of and a run of, so the slope is or. Verif this slope b using the slope formula with an two points on the graph. 6 Slope _ + or. Both methods result in the same slope. Choice B is correct. 6 8 run rise Rates of Change and Applications of Slope A rate of change shows the relationship between two quantities that are changing. This change can be constant or it can var. The rate of change of a linear function is constant and the same as the slope of the function. Slope can be used to find different rates of change, such as the grade of a road or the pitch of a roof. The greater the slope, the steeper the road or the roof pitch. For eample, suppose an architect draws the two roofs shown on the coordinate planes below. Roof A 6 Roof B 6,,, 6 6 6, 6 6 The coordinates of the left side of each roof drawing are shown. Use these coordinates and the slope formula to find the slope of each roof. The slope of roof A is _ +. The slope of roof B is _ 6+ 6. The slope of roof A is greater than the slope of roof B since.. So roof A is steeper than roof B. For an two points on a line _, + and _, + and, the slope of the line is. Unit 6 Coordinate Geometr
Tr this sample question. S- Rosemar grows a plant from seed. In weeks, the plant is centimeters tall. In 6 weeks, the plant is 7 centimeters tall. What is the average growth rate each week of this plant between weeks and 6? A cm B cm C 8 cm D cm To find the average growth rate each week, find the slope of the line between the points _, + and _6, 7+. Slope m 7 6. Choice A is correct. Finding Intercepts from Graphs On the graph of a line, the point where the line touches the -ais is the -intercept of the line. The point where the line touches the -ais is the -intercept of the line. For eample, on the graph below, the line touches the -ais at and the -ais at. The -intercept of this line is the point _, +. The -intercept is the point _, +. 6 6 6 If a line touches the -ais at a, the -intercept is the point _a, +. If a line touches the -ais at b, the -intercept is the point _, b+. Tr this sample question. S- Which statement best describes the graph of the line shown below? A The slope is positive and the -intercept is. B The slope is negative and the -intercept is. C The slope is positive and the -intercept is. D The slope is negative and the -intercept is. 6 Unit 6 Coordinate Geometr
The line on the graph slants upward from left to right, so the slope is positive. The line touches the -ais at and it touches the -ais at. So the -intercept is and the -intercept is. Choice A is correct. IT S YOUR TURN Read each problem. Circle the letter of the best answer.. A linear equation is graphed on the coordinate plane below. 6 6 6 6 What are the slope and -intercept of the graphed line? A The slope is, and the -intercept is. B The slope is, and the -intercept is. C The slope is, and the -intercept is. D The slope is, and the -intercept is.. A pole is placed against a house, 6 feet from the base of the wall. In this position, the pole has a slope of. What height off the ground does the top of the pole rest against the house? A. feet B feet C feet D feet. A snowstorm laid down more snow on top of an eisting base. The equation below can be used to find the total inches of snow, s, on the ground after an number of hours, h, of the storm. s.7h What does the number.7 represent in the equation? A the length of time in hours the snowstorm lasted B the inches of snow that fell per hour during the storm C the inches of snow on the ground after of an hour D the inches of snow on the ground at the beginning of the storm Unit 6 Coordinate Geometr 7
Read each problem. Circle the letter of the best answer.. The table below shows the rate charged to park in a parking garage. 6. In which graph does the line have a slope of and a -intercept of? Number of Hours Cost to Park ($)....7.... Melissa has parked her car in the garage for hours alread. How much more will it cost for her car to be parked for additional hour? A $.7 B $. C $. A B D $.7. What is the rate of change shown on the graph below? Temperature ( C) TEMPERATURE CHANGE OVER TIME Time (minutes) C D A C per minute B C per minute C C per minute D C per minute 8 Unit 6 Coordinate Geometr
Read each problem. Circle the letter of the best answer. 7. A balloon is released into the air at a height of meters, and rises at a rate of. meters per second. Which epression gives the number of seconds the balloon will take to reach a height of 8 meters? A._8+ B._8+ C._8 + D._8 + 8. Dimitri is buing a camera on an installment plan. He makes equal monthl paments. The equation below can be used to find the amount he owes after an number of months of paments. What does the number represent in the equation? A the total cost of the camera B the amount Dimitri pas each month C the amount Dimitri put down as a deposit D the number of months Dimitri will make paments 9. Two trains are approaching Chicago. The graph shows how each train s distance to Chicago is changing over time. Distance (miles) 8 DISTANCE TO CHICAGO Time (hours) The slope of the line describing train has slope 6. The slope of the line describing train has slope. Which statement best compares the two trains epected arrival times in Chicago? A Train will arrive minutes before train. B Train will arrive 6.7 minutes before train. C Train will arrive 6 minutes before train. D Train will arrive. minutes before train. Unit 6 Coordinate Geometr 9
Unit 6 Constructed-Response Review Read the problem. Write our answer for each part.. There is a linear relationship between the number of people in a group and the cost to enter a museum. The museum charges $ for two people and $8 for three people. A Write the equation in slope-intercept form that relates the number of people in a group to the cost of entering the museum. Show our work. Answer: B How much will it cost for a single individual to enter the museum? Answer: C How man people can enter the museum for $? Answer: Unit 6 Coordinate Geometr 6
Read the problem. Write our answer for each part.. The bottom of a ramp is placed feet from the edge of a stage platform. The ramp is feet off the ground when it is feet from the edge of the stage. Stage Platform Ramp ft ft ft A What is the slope of the ramp? Show our work. Answer: B How man feet off the ground is the top of the ramp? Answer: 6 Unit 6 Coordinate Geometr
C Write a linear equation in slope-intercept form that represents the height _+ of the ramp at an distance _+ from the stage. Answer: Unit 6 Coordinate Geometr 6