By S.L. Salas

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**Extra resources for Calculus One & Several Variables 8e instructor's solutions manual**

**Sample text**

2008 Value In Exercises 47–50, use the result of Exercise 46 to write an equation of the line in general form. 17 Linear Models and Rates of Change WRITING ABOUT CONCEPTS In Exercises 75–77, find the coordinates of the point of intersection of the given segments. Explain your reasoning. 75. Xmin = -6 Xmax = 6 Xscl = 1 Ymin = -4 Ymax = 4 Yscl = 1 (b, c) (−a, 0) (a, 0) Perpendicular bisectors 77. CAPSTONE 76. (b, c) (−a, 0) (a, 0) Medians (b, c) 60. A line is represented by the equation ax ϩ by ϭ 4.

14. g͑x͒ ϭ 4x2 15. g͑x͒ ϭ Ί6x 17. f ͑t͒ ϭ sec t 4 x2 28. f ͑x͒ ϭ Ϫ5 16. h͑x͒ ϭ Ϫ Ίx ϩ 3 18. h͑t͒ ϭ cot t 1 1 2 sin x Ϫ 1 Խx2 Ϫ 4Խ (b) f ͑0͒ (c) f ͑2͒ (d) f ͑t 2 ϩ 1͒ (c) f ͑1͒ (d) f ͑s 2 ϩ 2͒ (c) f ͑3͒ (d) f ͑b 2 ϩ 1͒ (c) f ͑5͒ (d) f ͑10͒ x 2 ϩ 2, x Յ 1 2 ϩ 2, x > 1 (a) f ͑Ϫ2͒ 30. f ͑x͒ ϭ x < 0 x Ն 0 Ά2x (b) f ͑0͒ ԽԽ ΆϪx ϩ 1, x Ն 1 x ϩ 1, x < 1 (b) f ͑1͒ Ίx ϩ 4, x Յ5 Ά͑x Ϫ 5͒ , x > 5 (a) f ͑Ϫ3͒ 3 (b) g͑2 ͒ (a) f ͑0͒ 26. g͑x͒ ϭ Ά2x2x ϩϩ 1,2, (a) f ͑Ϫ3͒ (a) g͑4͒ (b) g͑Ί5 ͒ 13. f ͑x͒ ϭ 27. f ͑x͒ ϭ 29.

The form that is better suited to sketching the graph of a line is the slopeintercept form of the equation of a line. THE SLOPE-INTERCEPT EQUATION OF A LINE The graph of the linear equation y ϭ mx ϩ b is a line having a slope of m and a y-intercept at ͑0, b͒. EXAMPLE 3 Sketching Lines in the Plane Sketch the graph of each equation. a. y ϭ 2x ϩ 1 b. y ϭ 2 c. 3y ϩ x Ϫ 6 ϭ 0 Solution a. Because b ϭ 1, the y-intercept is ͑0, 1͒. 18(a). b. Because b ϭ 2, the y-intercept is ͑0, 2͒. 18(b). c. Begin by writing the equation in slope-intercept form.