1.4 Assess Your Understanding

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1 40 CHAPTER Graphs.4 Assess Your Understanding Concepts and Vocabular. The slope of a vertical line is ; the slope of a horizontal line is.. Two nonvertical lines have slopes m and m, respectivel. The lines are parallel if and the are unequal; the lines are perpendicular if.. A horizontal line is given b an equation of the form, where b is the. 4. True or False: Vertical lines have an undefined slope. 5. True or False: The slope of the line = + 5 is. 6. True or False: Perpendicular lines have slopes that are reciprocals of one another. Skill Building In Problems 70, find the slope of the line and interpret the slope (, ) (, ) (, ) (, ) (, ) (, ) In Problems 8, plot each pair of points and determine the slope of the line containing them. Graph the line.., ; 4, 0. 4, ;, 4. -, ;, 4. -, ;, 5. -, -;, , ; -5, 7. -, ; -, - 8., 0;, In Problems 9 6, graph, b hand, the line containing the point P and having slope m. 9. P =, ; m = 0. P =, ; m = 4. P =, 4; m = -. P =, ; m = - 4 5

2 SECTION.4 ines 4. P = -, ; m = 0 4. P =, -4; m = 0 5. P = 0, ; slope undefined 6. P = -, 0; slope undefined In Problems 7, the slope and a point on a line are given. Use this information to locate three additional points on the line. Answers ma var. [Hint: It is not necessar to find the equation of the line. See Eample.] 7. Slope 4; point, 8. Slope ; point -, 9. Slope - point, -4 ; 4 0. Slope point -,. Slope -; point -, -. Slope -; point 4, ; In Problems 40, find an equation of the line (, ) (, ) (, ) (, ) (, ) (, ) (, ) (, ) (, ) = is parallel to = In Problems 4 64, find an equation for the line with the given properties. Epress our answer using either the general form or the slope intercept form of the equation of a line, whichever ou prefer. 4. Slope = ; containing the point -, 4. Slope = ; containing the point 4, - 4. Slope = - containing the point, Slope = containing the point, ; ; = 45. Containing the points, and -, 46. Containing the points -, 4 and, Slope = -; -intercept = intercept = ; -intercept = is parallel to = Slope = -; -intercept = - -intercept = -4; -intercept = 4 5. Slope undefined; containing the point, 4 5. Slope undefined; containing the point, 8 5. Parallel to the line = ; containing the point -, 54. Parallel to the line = -; containing the point -, = is perpendicular to = (, ) = is perpendicular to = 55. Parallel to the line - = -; containing the point 0, Parallel to the line - = -5; containing the point 0, Parallel to the line = 5; containing the point 4, 58. Parallel to the line = 5; containing the point 4, 59. Perpendicular to the line = + 4; containing the point, - 6. Perpendicular to the line + = ; containing the point -, Perpendicular to the line = - ; containing the point, - 6. Perpendicular to the line - = -5; containing the point 0, 4 6. Perpendicular to the line = 8; containing the point, Perpendicular to the line = 8; containing the point, 4

3 4 CHAPTER Graphs In Problems 65 84, find the slope and -intercept of each line. Graph the line b hand. Check our graph using a graphing utilit. 65. = = = = - + = = = = = = = 77. = = = 8. - = = = = 6 = 5 + = 0 In Problems 85 94, find the intercepts of the graph of each equation and graph the equation b hand = = = = = = = =. 6-4 = 4 - = Find an equation of the -ais. 96. Find an equation of the -ais. In Problems 9700, match each graph with the correct equation: = = = (d) = In Problems 004, write an equation of each line. Epress our answer using either the general form or the slope intercept form of the equation of a line, whichever ou prefer Applications and Etensions 05. Truck Rentals A truck rental compan rents a moving truck for one da b charging $9 plus $0.07 per mile. Write a linear equation that relates the cost C, in dollars, of renting the truck to the number of miles driven.what is the cost of renting the truck if the truck is driven 0 miles? 0 miles? 06. Cost Equation The fied costs of operating a business are the costs incurred regardless of the level of production. Fied costs include rent, fied salaries, and costs of buing machiner. The variable costs of operating a business are the costs that change with the level of output. Variable costs include raw materials, hourl wages, and electricit. Suppose that a manufacturer of jeans has fied costs of $500 and variable costs of $8 for each pair of jeans manufactured. Write a linear equation that relates the cost C, in dollars, of manufacturing the jeans to the number pairs of jeans manufactured. What is the cost of manufacturing 400 pairs of jeans? 740 pairs? 07. Cost of Sunda Home Deliver The cost to the Chicago Tribune for Sunda home deliver is approimatel $0.5 per newspaper with fied costs of $,070,000. Write an equation that relates the cost C and the number of copies delivered. SOURCE: Chicago Tribune, Wages of a Car Salesperson Dan receives $75 per week for selling new and used cars at a car dealership in Oak awn, Illinois. In addition, he receives 5% of the profit on an sales that he generates. Write an equation that relates Dan s weekl salar S when he has sales that generate a profit of dollars.

4 SECTION.4 ines Electricit Rates in Illinois Commonwealth Edison Compan supplies electricit to residential customers for a monthl customer charge of $7.58 plus 8.75 cents per kilowatt-hour for up to 400 kilowatt-hours. Write an equation that relates the monthl charge C,in dollars, to the number of kilowatt-hours used in a month, Graph this equation. What is the monthl charge for using 00 kilowatthours? (d) What is the monthl charge for using 00 kilowatthours? Interpret the slope of the line. SOURCE: Commonwealth Edison Compan, December Electricit Rates in Florida Florida Power & ight Compan supplies electricit to residential customers for a monthl customer charge of $5.5 plus cents per kilowatt-hour for up to 750 kilowatt-hours. Write an equation that relates the monthl charge C,in dollars, to the number of kilowatt-hours used in a month, Graph this equation. What is the monthl charge for using 00 kilowatthours? Discussion and Writing 7. Which of the following equations might have the graph shown? (More than one answer is possible.) + = = 6-4 = - (f) (g) - = - = - 5 = + (d) - = (h) = - + (d) What is the monthl charge for using 500 kilowatthours? Interpret the slope of the line. SOURCE: Florida Power & ight Compan, Januar 00.. Measuring Temperature The relationship between Celsius ( C) and Fahrenheit ( F) degrees of measuring temperature is linear. Find an equation relating C and F if 0 C corresponds to F and 00 C corresponds to F. Use the equation to find the Celsius measure of 70 F.. Measuring Temperature The Kelvin (K) scale for measuring temperature is obtained b adding 7 to the Celsius temperature. Write an equation relating K and C. Write an equation relating K and F (see Problem ).. Product Promotion A cereal compan finds that the number of people who will bu one of its products in the first month that it is introduced is linearl related to the amount of mone it spends on advertising. If it spends $40,000 on advertising, then 00,000 boes of cereal will be sold, and if it spends $60,000, then 00,000 boes will be sold. Write an equation describing the relation between the amount A spent on advertising and the number of boes sold. How much advertising is needed to sell 00,000 boes of cereal? Interpret the slope. 4. Show that the line containing the points a, b and b, a, a Z b, is perpendicular to the line =. Also show that the midpoint of a, b and b, a lies on the line =. 5. The equation - = C defines a famil of lines, one line for each value of C. On one set of coordinate aes, graph the members of the famil when C = -4, C = 0, and C =. Can ou draw a conclusion from the graph about each member of the famil? 6. Rework Problem 5 for the famil of lines C + = Which of the following equations might have the graph shown? (More than one answer is possible.) + = 6 - = - - = 6 (f) = = (g) = - (d) - = + 0 (h) = + 4

5 44 CHAPTER Graphs 9. The figure shows the graph of two parallel lines. Which of the following pairs of equations might have such a graph? - = + = 7 + = + = - - = - - = (d) - = - - = -4 + = + = -. The accepted smbol used to denote the slope of a line is the letter m. Investigate the origin of this smbolism. Begin b consulting a French dictionar and looking up the French word monter. Write a brief essa on our findings.. The term grade is used to describe the inclination of a road. How does this term relate to the notion of slope of a line? Is a 4% grade ver steep? Investigate the grades of some mountainous roads and determine their slopes. Write a brief essa on our findings. Steep 7% Grade 0. The figure shows the graph of two perpendicular lines. Which of the following pairs of equations might have such a graph? - = + = - - = 0 + = 0 - = + = - (d) - = + = - + = - + = -. Carpentr Carpenters use the term pitch to describe the steepness of staircases and roofs. How does pitch relate to slope? Investigate tpical pitches used for stairs and for roofs. Write a brief essa on our findings. 4. Can the equation of ever line be written in slope intercept form? Wh? 5. Does ever line have eactl one -intercept and one -intercept? Are there an lines that have no intercepts? 6. What can ou sa about two lines that have equal slopes and equal -intercepts? 7. What can ou sa about two lines with the same -intercept and the same -intercept? Assume that the -intercept is not If two lines have the same slope, but different -intercepts, can the have the same -intercept? 9. If two lines have the same -intercept, but different slopes, can the have the same -intercept?