154 Chapter 2 Linear Equations in Two Variables and Functions Concept 2: The Slope Formula For Exercises 13–30, use the slope formula to determine the slope of the line containing the two points. (See Examples 2–5.) 13. 16, 02 and 10, 32 14. 1 5, 02 and 10, 42 15. 1 2, 32 and 14, 72 16. 15,42 and 17. and 18. and 1 12, 32 14, 22 16, 82 11, 72 2, 52 19. 10.3, 1.12 and 1 0.1, 0.82 20. 10.4, 0.22 and 10.3, 0.12 21. 12, 32 and 12, 72 22. 1 1, 52 and 1 1, 02 23. 15, 12 and 1 13, 12 24. 8, 42 and 11, 42 a , 1b 3 2 25. and 10, 6.42 26. 11.1, 42 and 27. and a3 b 4 a1 b 2 a9 b 4 a2 1 b 3 6 28. and 29. and 30. and a2 31. Explain how to use the graph of a line to determine whether the slope of a line is positive, negative, zero, or 5 4 3 2 y , x 1 2 3 4 5 4 3 2 1 54321 1 2 3 4 5 1 2 3 4 5 5 4 3 2 1 54321 1 2 3 4 5 1 2 3 4 y x 5 4 3 2 1 54321 1 2 3 4 5 1 2 3 4 5 5 4 3 2 1 54321 1 2 3 4 5 1 2 3 4 y x 5 4 3 2 1 1 4 , 54321 1 2 3 4 5 1 2 3 4 5 43 36. 37. 38. Concept 3: Parallel and Perpendicular Lines For Exercises 39–44, the slope of a line is given. a. Find the slope of a line parallel to the given line. b. Find the slope of a line perpendicular to the given line. (See Example 6.) 39. m 5 40. m 3 41. 2 11 m 4 7 42. m 43. m 0 44. m is undefined. 1 10 , 2 5 , 2 1 3 , 7 3 a b , 3 2 , 1 2 b a7 2 , 4 3 1 b 1 3.2, 0.32 4.6, 4.12 y x 1 2 3 4 5 1 54 321 5 y x 5 y x 5 undefined. 32. If the slope of a line is how many units of change in y will be produced by 6 units of change in x? For Exercises 33–38, estimate the slope of the line from its graph. 33. 34. 35.
miller_intermediate_algebra_4e_ch1_3
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