Determine whether each pair of lines is parallel, perpendicular, or neither. a) x 6y 12 b) 4x y 1 c) 3x 2y 8 d) x 3 y 6x 9 2x 3y 6 15x 10y 2 y 2 Let’s learn how to write the equation of a line that is parallel or perpendicular to a given line. 6 Write an Equation of a Line That Is Parallel or Perpendicular to a Given Line YOU TRY 5 EXAMPLE 6 y 5 (4, 2) 5 5 y x 2 32 5 When working with parallel lines, be sure to verify that your final equation indicates the same slope as in the given line. x YOU TRY 6 A line contains the point (4, 2) and is parallel to the line y 3 2 equation of the line in slope-intercept form. Solution Let’s look at the graph on the left to help us understand what is happening in this example. We must fi nd the equation of the line in red. It is the line containing the point (4, 2) that is parallel to y 3 2 x 2. The line y 3 2 x 2 has m 3 2 . Therefore, the red line will have m We know the slope, 3 2 , and a point on the line, (4, 2), so we use the point-slope formula to fi nd its equation. Substitute 3 2 for m. Substitute (4, 2) for (x1, y1). y y1 m (x x1) y 2 3 2 (x 4) Substitute 4 for x1 and 2 for y1. y 2 3 2 x 6 Distribute. y 3 2 x 4 Add 2 to each side. The equation is y 3 2 x 4. A line contains the point (8, 5) and is parallel to the line y x 2. Write the 3 4 x 2 3 3 2 as well. . Write the equation of the line in slope-intercept form. 178 CHAPTER 4 Linear Equations in Two Variables and Functions www.mhhe.com/messersmith
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