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4.7 Parallel and Perpendicular Lines Parallel lines have the same slope. All vertical lines are parallel. All horizontal lines are parallel. Perpendicular lines have opposite reciprocal slopes. If m = 3, then the m = -1/3 If m = -2/3, then the m = 3/2 Write an equation of the line that is parallel to the graph of 2x + y = 5 and passes through the point (3,1). 2x y 5 y 2 x 5 Since y m x b the slope is -2. Using the point (3,1) and the parallel slope of -2, plug all into the point-slope form y y m( x x ) 1 1 y 1 2( x 3) y 1 2 x 6 Distribute Add 1 to both sides y 2 x 7 Write an equation of the line that is perpendicular to the graph of x - 6y = 2 and passes through the point (2,4). x 6y 2 6 y x 2 1 1 y x 6 3 1 m 6 m 6 Use pointslope form with slope = -6 and point given (2,4) y y1 m( x x1 ) y 4 6( x 2) y 4 6 x 12 y 6 x 16 Try These Two to Practice! Write the slope-intercept form of an equation for the line that passes through (4,-2) and is parallel to the graph of y 1 x 7 2 1 y x4 2 Write the slope-intercept for of an equation for the line that passes through (4,-1) and is perpendicular to the graph of 7 x 2 y 3 2 1 y x 7 7 Page 239 #1-7 odd 1. y = -2x -1 3. y = 2x – 5 5. Find the slope of segment AC 6/7 Find the slope of segment BD -7/6 They are opposite reciprocal slopes therefore they are perpendicular. 7. y 5 x 8 3 Homework #33: p. 240 10-30, 36, 37