254 Chapter 3 Graphing Linear Equations in Two Variables Writing an Equation of a Line Using Slope-Intercept Form Example 8 Write an equation of the line having a slope of 2 and passing through the point 13, 12. Solution: To find an equation of a line using slope-intercept form, it is necessary to find the values of m and b.The slope is given in the problem as Therefore, the slope-intercept form becomes 13, 12 y mx b y 2x b m 2. Because the point is on the line, it is a solution to the equation. Therefore, to find b, substitute the values of x and y from the ordered pair and solve the resulting equation. y 2x b 1 2132 b y 1 x 3. Substitute and Simplify and solve for b. 1 6 b 7 b 13, 12 Now with m and b known, the slope-intercept form is y 2x 7. TIP: The equation from Example 8 can be checked by graphing the line y 2x 7. The slope m 2 can be written as m . Therefore, to graph the line, start at the y-intercept (0, 7) and move up 2 units and to the right 1 unit. 21 The graph verifies that the line passes through the point 13, 12 as it should. 8765432 1 9 8 7 6 5 4 3 2 1 1 2 x 1 y y 2x 7 (3, 1) (0, 7) Skill Practice 13. Write an equation of the line having a slope of 3 and passing through the point 12, 52. Classroom Example: p. 258, Exercise 78 Answer 13. y 3x 11 Calculator Connections Topic: Using the ZSquare Option in Zoom In Example 6(a) we found that the equations y y 3x 4 13 and represent perpendicular x 3 lines.We can verify our results by graphing the lines on a graphing calculator. Notice that the lines do not appear perpendicular in the calculator display.That is, they do not appear to form a right angle at the point of intersection. Because many calculators have a rectangular screen, the standard viewing window is elongated in the horizontal direction.To eliminate this distortion, try using a ZSquare option, which is located under the Zoom menu. This feature will set the viewing window so that equal distances on the display denote an equal number of units on the graph.
miller_introductory_algebra_3e_ch1_3
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