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Parallel and Perpendicular Lines Objectives: Define parallel lines. Find equations of parallel lines. Define perpendicular lines Find equations of perpendicular lines.

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Parallel Lines Slopes of parallel lines are equal. Recall the steps of finding an equation of a line. –Find slope –Find the y-intercept –Write the equation –This is the same process when working with parallel and perpendicular lines.

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Find an equation of a line passing through (-2,5) that is parallel to 3x + 2y = 9 Find slope: –Get y by itself in the given equation 2y = 9 – 3x y = 9/2 – 3/2 x slope=-3/2 Find y-intercept: –Use a slope of -3/2 since the lines are parallel y = -3/2 x + b 5 = -3/2 (-2) + b 5 = 3 + b 2 = b Write equation: y = -3/2 x + 2

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Perpendicular Lines Perpendicular lines have negative reciprocal slopes. If a line has a slope of -1/2 the perpendicular line would have a slope of 2. If a line has a slope of 5/6 the perpendicular line would have a slope of -6/5 What would be the slope of a line perpendicular to a line with a slope of -7? 1/7

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Find the equation of the line passing through (-1,3) that is perpendicular to 3x – 2y = 8. 1.Find slope 1.Get y by itself: -2y = 8 – 3x y = -4 + 3/2 x 2.Slope is 3/2 so perpendicular slope is - 2/3 2.Find y-intercept 1.y = -2/3 x + b 3 = (-2/3)(-1) + b 3 = 2/3 + b 3 – 2/3 = b 7/3 = b 3.Write equation y = -2/3 x + 7/3

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Review concepts learned Parallel lines have equal slope Perpendicular lines have negative reciprocal slopes. To find an equation of a line –Find slope –Find y-intercept –Write equation

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Assignment Page 197 #7, 11, 13, 17, 21, 23, 25, 29, 33, 37

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