246 Chapter 3 Graphing Linear Equations in Two Variables Writing an Equation of a Line Perpendicular to Another Line Example 4 Use the point-slope formula to find an equation of the line passing through the point 13, 12 and perpendicular to the line 3x y 2. Write the final answer in slope-intercept form. Solution: The given line can be written in slope-intercept form as The slope of this line is Therefore, the slope of a line perpendicular to the given line is m 13 13 . 3. Apply the point-slope formula with y 3x 2. , and 1x1, y12 13, 12. Point-slope formula Substitute To write the final answer in slope-intercept form, simplify the equation and solve for y. Apply the distributive property. Add 1 to both sides. y y1 m1x x12 y 112 m 13 , x1 13 3, and y1 1. y 13 x 2 and y 3x 2 y 1 13 y 1 13 y 13 3x 132 4 1x 32 x 1 x 2 A sketch of the perpendicular lines is shown in y x 2 13, 13 12. Figure 3-33. Notice that the line passes through the point Skill Practice 4. Write an equation of the line passing through the point (10, 4) and perpendicular to the line x 2y 1 . 4. Different Forms of Linear Equations: A Summary A linear equation can be written in several different forms, as summarized in Table 3-3. 5 y 1 y 3x 2 21 54 3 1 2 3 4 5 1 2 3 4 5 x 4 3 (3, 1) 2 y x 2 13 Figure 3-33 Form Example Comments Standard Form A and B must not both be zero. Ax By C 4x 2y 8 Horizontal Line The slope is zero, and the y-intercept is y k y 4 (k is constant) (0, k). Vertical Line The slope is undefined, and the x-intercept x k x 1 (k is constant) is (k, 0). Slope-Intercept Form Solving a linear equation for y results in slope-intercept form.The coefficient of y mx b y 3x 7 Slope 3 the slope is m the x-term is the slope, and the constant y-intercept is (0, b) defines the location of the y-intercept. Point-Slope Formula This formula is typically used to build an equation of a line when a point on the line is known and the slope of the line is known. y-intercept is 10, 72 y y1 m1x x12 m 3 1x1, y12 14, 22 y 2 31x 42 Table 3-3 Answer 4. y 2x 16
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