Download presentation

1
**Warm Up Identify which lines are parallel.**

y = 6; y = 6x + 5; y = 6x – 7; y = -8 Identify which lines are perpendicular y = 3x – 4; y = x + 2; y = -1; x = 3

2
**Objectives Identify and graph parallel and perpendicular lines.**

Write equations to describe lines parallel or perpendicular to a given line.

3
Vocabulary parallel lines perpendicular lines

4
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.

5
Example 1 y = 3x + 8; (4, 10) Step 1 Find the slope of the line. y = 3x + 8 The slope is 3. The parallel line also has a slope of 3. Step 2 Write the equation in point-slope form. y – y1 = m(x – x1) Use the point-slope form. Substitute 3 for m, 4 for x1, and 10 for y1. y – 10 = 3(x – 4)

6
Example 1 Continued Step 3 Write the equation in slope-intercept form. y – 10 = 3(x – 4) y – 10 = 3x – 12) Distribute 3 on the right side. y = 3x – 2 Add 10 to both sides.

7
Example 2 y = x – 6; (5, 7) Step 1 Find the slope of the line. The slope is . y = x –6 The parallel line also has a slope of . Step 2 Write the equation in point-slope form. y – y1 = m(x – x1) Use the point-slope form.

8
Example 2 Continued Step 3 Write the equation in slope-intercept form. Distribute on the right side. Add 7 to both sides.

9
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.

10
Example 3 y = 2x – 5; (2, –1). Step 1 Find the slope of the line. y = 2x – 5 The slope is 2. The perpendicular line has a slope of because Step 2 Write the equation in point-slope form. y – y1 = m(x – x1) Use the point-slope form. Substitute for m, –1 for y1, and 2 for x1.

11
Example 3 Continued Step 3 Write the equation in slope-intercept form. Distribute on the right side. Subtract 1 from both sides.

12
Example 4 y = 5x; (–5, 3) Step 1 Find the slope of the line. y = 5x The slope is 5. The perpendicular line has a slope of because . Step 2 Write the equation in point-slope form. y – y1 = m(x – x1) Use the point-slope form.

13
Example 4 Continued Step 3 Write in slope-intercept form. Distribute on the right side. Add 3 to both sides.

14
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 = 4x + 5

Similar presentations

© 2023 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google