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Parallel and Perpendicular Lines 5-6 Parallel Lines • Parallel lines do not intersect! y = 2x + 4 and y = 2x + 3 will be parallel. • Parallel lines will have the same slope and different y-intercepts. Parallel Lines y = 2x + 4 be parallel. and y = 2x + 3 will Parallel Lines • Write the slope-intercept form of an equation for the line that passes through (-1,-2) and is parallel to the graph of y = -3x -2. THE SLOPE OF BOTH EQUATIONS WILL BE -3. y = mx + b (-1,2) SLOPE = -3 -2 = -3(-1) + b -2 = 3 + b -3 = -3 - 5 = b The equation is: y = -3x -5 • Example 2 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 ( The slope will be 1 ) 2 Parallel Lines • Write an equation of the line containing the point (0,6) and parallel to the line: The slope will be -3 y = -3x + 4 Perpendicular Lines • Perpendicular lines intersect and form rt. angles. The product of the slopes is -1. • Ex if a slope is -3, then the other slope of the line is 1 3 BECAUSE: -3 1 * 1 = -1 3 Perpendicular Lines • If a slope is -1 the line perpendicular 4 to that line must be 4 because: -1 * 4 = -4 = -1 4 1 4 Perpendicular Lines • Write the slope-intercept form of an equation that passes through (-2, 0) and is perpendicular to the graph of y = x -6 Slope of equation is 1, New slope must be -1 because 1 * -1 = -1 1 1 y = x -6 0 = -1(-2) + b 0=2 +b b = -2 Equation: y = -1x – 2 or y = -x -2 Perpendicular Lines • Write the slope-intercept form for an equation for the line that passes through (-1,3) and is perpendicular to 2x + 4y = 12 a) Solve for y in terms of x: 2x + 4y = 12 b) Substitute values in for x, y, and m Practice • Write the slope-intercept form of an equation of the line that passes through the given point and is ll to the graph of the equation. 1) (3,2), y = 3x + 4 2) (-1,-2) y = -3x + 5 Practice • Write the slope-intercept form of an equation of the line that passes through the given point and is ll to the graph of the equation. 3) (3,2), y = 3x + 4 4) (-5,-1), 2y = 2x -4 Practice • Write the slope-intercept form of an equation of the line that passes through the given point and is perpd.( l ) to the graph of each equation. 5) (-3,-2), y = x + 2 6) (4,-1), y = 2x -4 Practice • Write the slope-intercept form of an equation of the line that passes through the given point and is l to the graph of each equation. 7) (-5,1), y = - 5 x -7 3 8) (-2,2) 6x + 3y = -9 Guided Practice • See pg 295 #4