Day 8

Writing Linear Equations

Given Slope and a Point

EMAT6690

by Chris Reid

On day 7 of this unit, you learned to write an equation for a line given the slope of the line and the y-intercept of the line.

This lesson will teach you how to write the equation of a line given the slope of the line and any point on the line.

Example:

Write the equation of the line that passes through the point (4, -2) and has a slope of 2. Write the equation in slope-intercept form.

Solution:

The slope m is 2. Find the y-intercept b using m=2 and the point (4, -2) where x=4 and y=-2.

Substitute into the slope-intercept equation.

y = mx + b

-2 = 2(4) + b

-2 = 8 + b

-10 = b

Write the equation using m=2 and b=-10.

y = 2x + (-10)

y = 2x - 10

The equation of the line is y = 2x - 10.

Assignment:

Write an equation of the line that passes through the point and has the given slope. Write the equation in slope-intercept form.

1. (1, 2), m = 4

2. (-2, 3), m = -2

3. (-4, 3), m = 0

4. (3, -2), m = 4

5. (2, 5), m = 1/2

6. (-3, 2), m = -1/3

7. (0, -8), m = 6

8. (5, 0), m = -2

9. (-2, 2), m = 4

10. (-3, -5), m = -2