Section 2.2 Slope of a Line and Rate of Change 145 60. Which of the lines defined here has only one unique intercept? a. b. c. d. y 5 x 2y 0 3x 4 2 x 3y 6 Expanding Your Skills For Exercises 61–64, find the x- and y-intercepts. x a y b x 7 y 4 x 2 y 3 61. 62. 63. 64. Ax By C 1 1 1 Graphing Calculator Exercises For Exercises 65–68, solve the equation for y. Use a graphing calculator to graph the equation on the standard viewing window. 65. 2x 3y 7 66. 4x 2y 2 67. 3y 9 68. 2y 10 0 For Exercises 69–72, use a graphing calculator to graph the lines on the suggested viewing window. 1 3 1 2 69. y 70. x 12 71. 72. y 2x 4y 1 5y 4x 1 x 10 30 x 10 10 x 40 1 x 1 0.5 x 0.5 15 y 5 10 y 20 1 y 1 0.5 y 0.5 For Exercises 73–74, graph the lines in parts (a)–(c) on the same viewing window. Compare the graphs.Are the lines exactly the same? 73. a. y x 3 74. a. y 2x 1 Slope of a Line and Rate of Change Section 2.2 1. Introduction to the Slope of a Line In Section 2.1, we learned how to graph a linear equation and to identify its x- and y-intercepts. In this section, we learn about another important feature of a line called the slope of a line. Geometrically, slope measures the “steepness” of a line. Figure 2-12 shows a set of stairs with a wheelchair ramp to the side. Notice that, even though the stairs and ramp both rise the same vertical distance, the stairs are steeper than the ramp. This is because the stairs rise 3 ft over a shorter horizontal distance than the ramp. 4 ft 3 ft 3 ft 18 ft Figure 2-12 Concepts 1. Introduction to the Slope of a Line 2. The Slope Formula 3. Parallel and Perpendicular Lines 4. Applications and Interpretation of Slope b. b. c. y x 2.9 c. y 2.1x 1 y x 3.1 y 1.9x 1
miller_intermediate_algebra_4e_ch1_3
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