5 8 Slopes of Parallel and Perpendicular Lines

5 -8 Slopes of Parallel and Perpendicular Lines Warm Up Identify which lines are parallel. 1. y = 6; y = 6 x + 5; y = 6 x – 7; y = -8 Identify which lines are perpendicular 2. y = 3 x – 4; y = x + 2; y = -1; x = 3 Holt Algebra 1

5 -8 Slopes of Parallel and Perpendicular Lines Objectives Identify and graph parallel and perpendicular lines. Write equations to describe lines parallel or perpendicular to a given line. Holt Algebra 1

5 -8 Slopes of Parallel and Perpendicular Lines Vocabulary parallel lines perpendicular lines Holt Algebra 1

5 -8 Slopes of Parallel and Perpendicular Lines Directions: Write an equation in slope-intercept form for the line that is parallel to the given line and that passes through the given point. Holt Algebra 1

5 -8 Slopes of Parallel and Perpendicular Lines Example 1 y = 3 x + 8; (4, 10) Step 1 Find the slope of the line. The slope is 3. y = 3 x + 8 The parallel line also has a slope of 3. Step 2 Write the equation in point-slope form. y – y 1 = m(x – x 1) Use the point-slope form. y – 10 = 3(x – 4) Substitute 3 for m, 4 for x 1, and 10 for y 1. Holt Algebra 1

5 -8 Slopes of Parallel and Perpendicular Lines Example 1 Continued Step 3 Write the equation in slope-intercept form. y – 10 = 3(x – 4) y – 10 = 3 x – 12) y = 3 x – 2 Holt Algebra 1 Distribute 3 on the right side. Add 10 to both sides.

Slopes of Parallel and Perpendicular Lines 5 -8 Example 2 y= x – 6; (5, 7) Step 1 Find the slope of the line. y= x – 6 The slope is The parallel line also has a slope of . . Step 2 Write the equation in point-slope form. y – y 1 = m(x – x 1) Use the point-slope form. Holt Algebra 1

5 -8 Slopes of Parallel and Perpendicular Lines Example 2 Continued Step 3 Write the equation in slope-intercept form. Distribute on the right side. Add 7 to both sides. Holt Algebra 1

5 -8 Slopes of Parallel and Perpendicular Lines Directions: Write an equation in slope-intercept form for the line that is perpendicular to the given line and that passes through the given point. Holt Algebra 1

5 -8 Slopes of Parallel and Perpendicular Lines Example 3 y = 2 x – 5; (2, – 1). Step 1 Find the slope of the line. The slope is 2. y = 2 x – 5 The perpendicular line has a slope of because Step 2 Write the equation in point-slope form. Use the point-slope form. y – y 1 = m(x – x 1) Holt Algebra 1 Substitute and 2 for x 1. for m, – 1 for y 1,

5 -8 Slopes of Parallel and Perpendicular Lines Example 3 Continued Step 3 Write the equation in slope-intercept form. Distribute on the right side. Subtract 1 from both sides. Holt Algebra 1

5 -8 Slopes of Parallel and Perpendicular Lines y = 5 x; (– 5, 3) Example 4 Step 1 Find the slope of the line. The slope is 5. y = 5 x The perpendicular line has a slope of because . Step 2 Write the equation in point-slope form. y – y 1 = m(x – x 1) Use the point-slope form. Holt Algebra 1

5 -8 Slopes of Parallel and Perpendicular Lines Example 4 Continued Step 3 Write in slope-intercept form. Distribute on the right side. Add 3 to both sides. Holt Algebra 1

5 -8 Slopes of Parallel and Perpendicular Lines Lesson Summary Write an equation is slope-intercept form for the line described. 1. contains the point (8, – 12) and is parallel to 2. contains the point (4, – 3) and is perpendicular to y = 4 x + 5 Holt Algebra 1