Day 9

Writing Linear Equations

Given Two Points

EMAT6690

by Chris Reid

This lesson will teach you to write the equation of a lie given any two points on that line.

Process:

Step 1: Find the slope of the line.

Step 2: Find the y-intercept of the line.

Step 3: Write the equation of the line using slope-intercept form.

Example:

Write an equation of the line that passes through the points

(3, 1), and (6, -2).

Solution:

Step 1: Find the slope of the line.

Let (X1, Y1) = (3, 1) and (X2, Y2) = (6, -2). Substitute each value into the equation for slope.

The slope of the line is -1.

Step 2: Find the y-intercept of the line.

Select one of the given points, (3, 1) and let x=3, y=1, and m = -1. Substitute each value into the slope-intercept equation.

y = mx + b

1 = -1(3) + b

1 = -3 + b

4 = b

The y-intercept of the line is 4.

Step 3: Write the equation in slope-intercept form.

Using m = -1 and b = 4, substitute into the slope-intercept equation.

y = mx + b

y = -1x + 4

The simplified form of the equation of the line is

y = -x + 4.

Assignment:

Write an equation of the line passing through each pair of points. Write the equation in slope-intercept form.

1. (3, 14) and (1, 4)

2. (-6, -9) and (-5, 10)

3. (12, -7) and (10. -3)

4. (-6, -5) and (2, 3)

5. (4, -2) and (5, 4)

6. (-4, 9) and (-3, 8)

7. (1/2, -1/2) and (1/4, 3/4)

8. (-1, 0) and (-5, -3)

9. (-3, 7) and (1, 7)

10. (1, 2) and (3, 4)