264 Chapter 3 Graphing Linear Equations in Two Variables 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 Apply the point-slope formula with y 3x 2. 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 , x1 3, and y1 1. 13 y 13 x 2 and y 3x 2 A sketch of the perpendicular lines is shown in Figure 3-33. Notice that the line y x 2 13 passes through the point 13, 12. y 13 x 2 y 1 13 x 1 y 1 13 1x 32 m 13 3x 1324 m 13 , and 1x1, y12 13, 12. 13 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 4. Different Forms of Linear Equations: A Summary A linear equation can be written in several different forms, as summarized in Table 3-3. 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 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. Slope 3 y-intercept is 10, 72 y y1 m1x x12 m 3 1x1, y12 14, 22 y 2 31x 42 Table 3-3 Skill Practice 4. Write an equation of the line passing through the point (10, 4) and perpendicular to the line x 2y 1. Classroom Example: p. 267, Exercise 34 Answers 4. y 2x 16 5. The point-slope formula requires a value for the slope and a vertical line has an undefined slope. 6. The form x k must be used. Then the appropriate value is substituted for k. Figure 3-33 Concept Connections 5. Explain why the point-slope formula cannot be used to write an equation for a vertical line. 6. Explain how to write an equation for a vertical line.
miller_introductory_algebra_3e_ch1_3
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