Download presentation

Presentation is loading. Please wait.

Published byKassidy Pocklington Modified over 8 years ago

1
**Write an equation given the slope and a point**

EXAMPLE 2 Write an equation given the slope and a point Write an equation of the line that passes through (5, 4) and has a slope of – 3. SOLUTION Because you know the slope and a point on the line, use point-slope form to write an equation of the line. Let (x1, y1) = (5, 4) and m = – 3. y – y1 = m(x – x1) Use point-slope form. y – 4 = – 3(x – 5) Substitute for m, x1, and y1. y – 4 = – 3x + 15 Distributive property y = – 3x + 19 Write in slope-intercept form.

2
EXAMPLE 3 Write equations of parallel or perpendicular lines Write an equation of the line that passes through (–2,3) and is (a) parallel to, and (b) perpendicular to, the line y = –4x + 1. SOLUTION a. The given line has a slope of m1 = –4. So, a line parallel to it has a slope of m2 = m1 = –4. You know the slope and a point on the line, so use the point-slope form with (x1, y1) = (– 2, 3) to write an equation of the line.

3
**Write equations of parallel or perpendicular lines**

EXAMPLE 3 Write equations of parallel or perpendicular lines y – y1 = m2(x – x1) Use point-slope form. y – 3 = – 4(x – (– 2)) Substitute for m2, x1, and y1. y – 3 = – 4(x + 2) Simplify. y – 3 = – 4x – 8 Distributive property y = – 4x – 5 Write in slope-intercept form.

4
**Write equations of parallel or perpendicular lines**

EXAMPLE 3 Write equations of parallel or perpendicular lines b. A line perpendicular to a line with slope m1 = – 4 has a slope of m2 = – = . Use point-slope form with (x1, y1) = (– 2, 3) 1 4 m1 y – y1 = m2(x – x1) Use point-slope form. y – 3 = (x – (– 2)) 1 4 Substitute for m2, x1, and y1. y – 3 = (x +2) 1 4 Simplify. y – 3 = x + 1 4 2 Distributive property y = x + 1 4 2 Write in slope-intercept form.

5
**GUIDED PRACTICE GUIDED PRACTICE for Examples 2 and 3**

4. Write an equation of the line that passes through (– 1, 6) and has a slope of 4. SOLUTION Because you know the slope and a point on the line, use the point-slope form to write an equation of the line. Let (x1, y1) = (–1, 6) and m = 4 y – y1 = m(x – x1) Use point-slope form. y – 6 = 4(x – (– 1)) Substitute for m, x1, and y1. y – 6 = 4x + 4 Distributive property y = 4x + 10 Write in slope-intercept form.

6
**GUIDED PRACTICE GUIDED PRACTICE for Examples 2 and 3**

5. Write an equation of the line that passes through (4, –2) and is (a) parallel to, and (b) perpendicular to, the line y = 3x – 1. SOLUTION The given line has a slope of m1 = 3. So, a line parallel to it has a slope of m2 = m1 = 3. You know the slope and a point on the line, so use the point - slope form with (x1, y1) = (4, – 2) to write an equation of the line. y – y1 = m2(x – x1) Use point-slope form. y – (– 2) = 3(x – 4) Substitute for m2, x1, and y1. y + 2 = (x – 4) Simplify. y + 2 = 3x – 12 Distributive property y = 3x – 14 Write in slope-intercept form.

7
**Use point - slope form with (x1, y1) = (4, – 2)**

GUIDED PRACTICE GUIDED PRACTICE for Examples 2 and 3 b. A line perpendicular to a line with slope m1 = 3 has a slope of m2 = – = – 1 1 3 m1 Use point - slope form with (x1, y1) = (4, – 2) y – y1 = m2(x – x1) Use point-slope form. y – (– 2) = – (x – 4) 1 3 Substitute for m2, x1, and y1. y + 2 = – (x – 4) 1 3 Simplify. 4 3 y + 2 = – x – 1 Distributive property y = – x – 1 3 2 Write in slope-intercept form.

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