5.5: Writing Equations of Parallel and Perpendicular Lines Do NOW Write the following as an equation in point-slope form (7, –1), m = –6 (–6, 6), m = 3/2 (–4, –1), (6, –7) 12/7/2018 11:20 PM 5.5: Writing Equations of Parallel and Perpendicular Lines

5.5: Writing Equations of Parallel and Perpendicular Lines Worksheet Key 12/7/2018 11:20 PM 5.5: Writing Equations of Parallel and Perpendicular Lines

Parallel & Perpendicular Lines Section 5.5 12/7/2018 11:20 PM 5.5: Writing Equations of Parallel and Perpendicular Lines

5.5: Writing Equations of Parallel and Perpendicular Lines Definitions Linear equation: An equation whose graph is a line Slope is a non-vertical line of the vertical change to the horizontal change between two points of a line Y-intercept is where the line crosses the y-axis 12/7/2018 11:20 PM 5.5: Writing Equations of Parallel and Perpendicular Lines

5.5: Writing Equations of Parallel and Perpendicular Lines Slope Equation: 12/7/2018 11:20 PM 5.5: Writing Equations of Parallel and Perpendicular Lines

5.5: Writing Equations of Parallel and Perpendicular Lines Recall Slope Y-intercept 12/7/2018 11:20 PM 5.5: Writing Equations of Parallel and Perpendicular Lines

5.5: Writing Equations of Parallel and Perpendicular Lines Steps Determine the first line of the slopes by putting it in Slope-Intercept form Determine the second line of the slopes Compare the slopes and determine whether is parallel, perpendicular, or neither slopes Parallel Slopes: SAME SLOPE Perpendicular Slopes: OPPOSITE SIGN RECIPROCAL SLOPE Neither Slopes: Does not fit either A or B PARALLEL Slopes PERPENDICULAR Slopes PARA||EL PERPEND CULAR 12/7/2018 11:20 PM 5.5: Writing Equations of Parallel and Perpendicular Lines 7

5.5: Writing Equations of Parallel and Perpendicular Lines Parallel Lines 12/7/2018 11:20 PM 5.5: Writing Equations of Parallel and Perpendicular Lines 8

5.5: Writing Equations of Parallel and Perpendicular Lines 12/7/2018 11:20 PM 5.5: Writing Equations of Parallel and Perpendicular Lines 9

5.5: Writing Equations of Parallel and Perpendicular Lines Example 1 Line 1 contains points of (4, –1) and (7, –2) Line 2 contains points of (–2, 1) and (1, 0) Is it parallel, perpendicular, or neither? x y 4 –1 7 –2 x y –2 1 Parallel 12/7/2018 11:20 PM 5.5: Writing Equations of Parallel and Perpendicular Lines

5.5: Writing Equations of Parallel and Perpendicular Lines Example 2 Line 1 contains points of (1, 4) and (2, 7) Line 2 contains points of (1, 0) and (–2, 1) Is it parallel, perpendicular, or neither? x y 1 4 2 7 x y 1 –2 Perpendicular 12/7/2018 11:20 PM 5.5: Writing Equations of Parallel and Perpendicular Lines

5.5: Writing Equations of Parallel and Perpendicular Lines Example 3 Line 1 contains points of (–4, –8) and (0, –6) Line 2 contains points of (0, 2) and (1, 4) Is it parallel, perpendicular, or neither? x y –4 –8 –6 x y 2 1 4 Neither 12/7/2018 11:20 PM 5.5: Writing Equations of Parallel and Perpendicular Lines

5.5: Writing Equations of Parallel and Perpendicular Lines Your Turn Line 1 contains points of (4, 3) and (3, –1) Line 2 contains points of (–3, 3) and (1, 2) Is it parallel, perpendicular, or neither? Perpendicular 12/7/2018 11:20 PM 5.5: Writing Equations of Parallel and Perpendicular Lines

5.5: Writing Equations of Parallel and Perpendicular Lines Example 4 Determine whether the lines are parallel, perpendicular, or neither of Perpendicular 12/7/2018 11:20 PM 5.5: Writing Equations of Parallel and Perpendicular Lines 14

5.5: Writing Equations of Parallel and Perpendicular Lines Example 5 Determine whether the lines are parallel, perpendicular, or neither of Parallel 12/7/2018 11:20 PM 5.5: Writing Equations of Parallel and Perpendicular Lines 15

5.5: Writing Equations of Parallel and Perpendicular Lines Example 6 Determine whether the lines are parallel, perpendicular, or neither of Parallel 12/7/2018 11:20 PM 5.5: Writing Equations of Parallel and Perpendicular Lines 16

5.5: Writing Equations of Parallel and Perpendicular Lines Your Turn Determine whether the lines are parallel, perpendicular, or neither of Neither 12/7/2018 11:20 PM 5.5: Writing Equations of Parallel and Perpendicular Lines 17

Given Point and Equation Rewrite the equation in Slope Intercept form Apply the appropriate slope Plug in points (x and y) and solve for the y-intercept Simplify Check using the Graphing Calculator 12/7/2018 11:20 PM 5.5: Writing Equations of Parallel and Perpendicular Lines

5.5: Writing Equations of Parallel and Perpendicular Lines Example 7 Write an equation of a line that contains the point (2, –3) and is parallel to the line y = –2x + 8 in slope-intercept form. 12/7/2018 11:20 PM 5.5: Writing Equations of Parallel and Perpendicular Lines

5.5: Writing Equations of Parallel and Perpendicular Lines Example 8 Write an equation of a line that contains the point (2, –3) and is perpendicular to the line y = –2x + 8 in slope-intercept form. 12/7/2018 11:20 PM 5.5: Writing Equations of Parallel and Perpendicular Lines

5.5: Writing Equations of Parallel and Perpendicular Lines Example 9 Write an equation of a line that contains the point (3, –3) and is parallel to the line y = x + 5 in slope-intercept form. 12/7/2018 11:20 PM 5.5: Writing Equations of Parallel and Perpendicular Lines

5.5: Writing Equations of Parallel and Perpendicular Lines Your Turn Write an equation of a line that contains the point (3, –3) and is perpendicular to the line y = x + 5 in slope-intercept form. 12/7/2018 11:20 PM 5.5: Writing Equations of Parallel and Perpendicular Lines

5.5: Writing Equations of Parallel and Perpendicular Lines Example 10 Write an equation of a line that is parallel to the line x = 5 and contains the point of (4, 2) 12/7/2018 11:20 PM 5.5: Writing Equations of Parallel and Perpendicular Lines

5.5: Writing Equations of Parallel and Perpendicular Lines Example 11 Write an equation of a line that is perpendicular to the line x = 5 and contains the point of (4, 2) 12/7/2018 11:20 PM 5.5: Writing Equations of Parallel and Perpendicular Lines

5.5: Writing Equations of Parallel and Perpendicular Lines Example 12 Write an equation of a line that is parallel to the line y = 5 and contains the point of (4, 2) 12/7/2018 11:20 PM 5.5: Writing Equations of Parallel and Perpendicular Lines

5.5: Writing Equations of Parallel and Perpendicular Lines Your Turn Write an equation of a line that is perpendicular to the line y = 5 and contains the point of (4, 2) 12/7/2018 11:20 PM 5.5: Writing Equations of Parallel and Perpendicular Lines

5.5: Writing Equations of Parallel and Perpendicular Lines Assignment Worksheet 12/7/2018 11:20 PM 5.5: Writing Equations of Parallel and Perpendicular Lines