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

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.

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

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

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 = /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

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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