288 Chapter 3 Graphing Linear Equations in Two Variables 4x 3y 6 2y 6x 3 2 , 0b x-intercept: a ; y-intercept: (0, 2) 4 ft 10 ft y 14 6. Given the equation x 2, complete the table. Plot the ordered pairs and graph the line through the points to represent the set of all solutions to the equation. x y 0 4 6 2 1 12 6 7 5 4 y 3 2 1 321 1 2 3 4 5 (4, 1) (0, 2) (6, ) 1 3 4 5 x 2 12 x-intercept: (0, 0); y-intercept: (0, 0) x-intercept: (4, 0); y-intercept: none x-intercept: none; y-intercept: (0, 3) For Exercises 7–10, graph the equations. 7. 8. y 3x 2 2x 5y 0 54 3 5 4 3 2 1 21 y y 3x 2 9. 10. 2524 23 5 4 3 2 1 21 y 1 2 3 4 5 5 4 3 2 1 2221 y 21 22 23 24 25 2x 5y 0 3 4 y 5 x 2 2 5 4 3 2 1 21 y 3x 2y 8 For Exercises 11 and 12, determine whether the equation represents a horizontal or vertical line. Then graph the line. 11. 6y 18 12. 5x 1 8 x 1 2 3 4 5 54 3 1 2 3 4 5 x 1 2 3 4 5 y 3 4 3x 2y 8 x 2 x 1 2 3 4 5 54 3 1 2 3 4 5 x 1 2 3 4 5 For Exercises 13–16, determine the x- and y-intercepts if they exist. 13. 14. 15. 16. 17. What is the slope of the hill? x 4 y 3 0 Horizontal Vertical 5 4 y 1 543 21 1 2 3 4 5 2 4 5 x 3 2 1 6y 18 3 5 4 543 1 2 3 4 5 2 3 4 5 5x 1 8 1 21 y x 3 2 1 2 5 18. a. Find the slope of the line that passes through 12, 02 15, 12 1 the points and . b. Find the slope of the line 4x 3y 9 . 19. a. What is the slope of a line parallel to the line x 4y 16? b. What is the slope of a line perpendicular to the line 20. a. What is the slope of the line x 5? Undefined b. What is the slope of the line y 3? 0 21. Carlos called a local truck rental company and got quotes for renting a truck. He was told that it would cost $41.95 to rent a truck for one day to travel 20 miles. It costs $89.95 to rent the truck for one day to travel 100 miles. Let x represent the number of miles driven and y represent the cost of the rental. 100 80 60 40 20 a. Using the ordered pairs (20, 41.95) and (100, 89.95), find the slope of the line. m 0.6 b. Interpret the slope in the context of this problem. The cost of renting a truck increases at a rate of $0.60 per mile. 22. Determine whether the lines through the given points are parallel, perpendicular, or neither. l1: 11, 42, 11, 22 l2: 10, 52, 12, 112 Parallel 0 20 40 60 80 100 120 0 Number of Miles Driven Cost ($) y Price of Renting a Truck for a Day x (20, 41.95) (100, 89.95) x 4y 16? 4 3 4 3 1 4 Writing Translating Expression Geometry Scientific Calculator Video
miller_introductory_algebra_3e_ch1_3
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