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3.8 Slopes of Parallel and Perpendicular Lines SOL G3b Objectives: TSW … Relate slope to perpendicular and parallel lines. Applying slope to verify and determine whether lines are parallel or perpendicular Write equations of lines that are perpendicular or parallel to each other.

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Key Concepts: Slopes of Parallel Lines If two nonvertical lines are parallel, then their slopes are equal. If the slope of two distinct nonvertical lines are equal, then the lines are parallel. Any two vertical lines or horizontal lines are parallel.

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Example 1: Check for parallel lines. Are lines l 1 and l 2 parallel? Explain? l1l1 l2l2 Since the two slopes are not equal Then the lines are not parallel

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Example 2: Check for parallel lines. Are lines l 3 contains A(-13, 6) and B(-1, 2). Line l 4 contains C(3, 6) and D(6, 7). Are l 3 and l 4 parallel? Explain? l3l3 l4l4 Since the two slopes are not equal Then the lines are not parallel

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Writing Equations of Parallel Lines Identify the slope of the given line. Since the lines are parallel; the slopes are the same (equal) You know a point and the slope for the new line. Use point-slope form to write the equation.

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Example 3: Writing Equations of Parallel Lines What is an equation of the line parallel to y = -3x – 5 that contains point (-1, 8)? m = -3 y – y1 = m(x – x 1 ) y – 8 = -3(x – (-1)) y – 8 = -3(x + 1) Point-slope form Substitute -3 for m, 8 for y 1 and -1 for x 1

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Example 4: Writing Equations of Parallel Lines What is an equation of the line parallel to y = -x – 7 that contains point (-5, 3)? m = -1 y – y 1 = m(x – x 1 ) y – 3 = - (x – (-5)) y – 3 = -(x + 5) Point-slope form Substitute -1 for m, 3 for y 1 and -5 for x 1

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Key Concepts: Slopes of Perpendicular Lines If two nonvertical lines are perpendicular, then the product of their slopes is -1. (negative reciprocals) If the slopes of two lines have a product of -1, then the lines are perpendicular. Any horizontal line and vertical line are perpendicular.

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Example 5: Check for parallel lines. Lines l 1 and l 2 are neither horizontal nor vertical? Are they perpendicular? Explain? l1l1 l2l2 Since the product of the two slopes Equal -1 then the lines are perpendicular

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Example 6: Check for perpendicular lines. Are lines l 3 contains A(2, 7) and B(3, -1). Line l 4 contains C(-2, 6) and D(8, 7). Are l 3 and l 4 parallel? Explain? l3l3 l4l4 Since the product of the two slopes do not equal -1 Then the lines are not perpendicular

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Writing Equations of Perpendicular Lines Identify the slope of the given line. Recall perpendicular have a product of -1. Negative Reciprocals. You know a point and the slope for the new line. Use point-slope form to write the equation.

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Example 7: Writing Equations of Perpendicular Lines What is an equation of the line perpendicular to y = x – 5 that contains point (15, -4)? m = -5 y – y 1 = m(x – x 1 ) y – (-4) = -5(x – 15) y + 4 = -5(x - 15) Point-slope form Substitute -5 for m, -4 for y 1 and 15 for x 1 Negative reciprocal

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Example 8: Writing Equations of Perpendicular Lines What is an equation of the line perpendicular to y = -3x – 5 that contains point (-3, 7)? m = y – y 1 = m(x – x 1 )Point-slope form Substitute for m, 7 for y 1 and -3 for x 1 Negative reciprocal y – 7 = (x – (-3)) y - 7 = (x + 3)

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HW: pg 201 – 203 # 7 – 21 odd, 27, 29, 41

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