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.
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.
Example 1: Check for parallel lines. Are lines l1 and l2 parallel? Explain? l1 l2 Since the two slopes are not equal Then the lines are not parallel
Example 2: Check for parallel lines. Are lines l3 contains A(-13, 6) and B(-1, 2). Line l4 contains C(3, 6) and D(6, 7). Are l3 and l4 parallel? Explain? l3 l4 Since the two slopes are not equal Then the lines are not parallel
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.
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 – x1) Point-slope form y – 8 = -3(x – (-1)) Substitute -3 for m, 8 for y1 and -1 for x1 y – 8 = -3(x + 1)
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 – y1 = m(x – x1) Point-slope form y – 3 = - (x – (-5)) Substitute -1 for m, 3 for y1 and -5 for x1 y – 3 = -(x + 5)
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.
Example 5: Check for parallel lines. Lines l1 and l2 are neither horizontal nor vertical? Are they perpendicular? Explain? l1 l2 Since the product of the two slopes Equal -1 then the lines are perpendicular
Example 6: Check for perpendicular lines. Are lines l3 contains A(2, 7) and B(3, -1). Line l4 contains C(-2, 6) and D(8, 7). Are l3 and l4 parallel? Explain? l3 l4 Since the product of the two slopes do not equal -1 Then the lines are not perpendicular
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.
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 Negative reciprocal y – y1 = m(x – x1) Point-slope form y – (-4) = -5(x – 15) Substitute -5 for m, -4 for y1 and 15 for x1 y + 4 = -5(x - 15)
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 = Negative reciprocal y – y1 = m(x – x1) Point-slope form y – 7 = (x – (-3)) Substitute for m, 7 for y1 and -3 for x1 y - 7 = (x + 3)
HW: pg 201 – 203 # 7 – 21 odd, 27, 29, 41