1. Writing the Equation of a Line
Section 3.4
Writing the Equation of a Line

2. To Find an Equation of a Line
1. Write the slope-intercept form of the equation of a line: y = mx + b.
2. Find m (if not given).
3. Substitute the given values of x, y, and m into the equation.
4. Solve for b.
5. Use the values of b and m to write the equation in the form y = mx + b.

3. Example
Find an equation of the line that passes through (4, 3) with a slope of 5. m = 5, x = 4, y = 3 y = mx + b 3 = (5)(4) + b 23 = b The equation of the line is y = 5x  23.

4. Example
Find an equation of the line that passes through (2, 1) and (7, 4). Find the slope of the line.
y = mx + b
The equation of the line is

5. Example
Find the equation of the line for the following graph. Find the y-intercept. Find the slope. x y 1 2 3 4 1 2 3 4
(0, 2)
Change in y = 2
(3, 0)
Change in x = 3
The equation of the line is

6. Parallel Lines Parallel lines are two straight lines that never touch.
Parallel lines have the same slope but different y-intercepts. x y
Slope m1
m1 = m2
Slope m2

7. Perpendicular Lines
Perpendicular lines are two lines that meet in a 90° angle.
Perpendicular lines have slopes whose product is –1.
If m1 and m2 are slope of perpendicular lines, then
m1m2 =  1 x y
Slope m2
m1 =
Slope m1

8. Example
Line c has a slope of 1/2. If line d is parallel to line c, what is its slope? Parallel lines have the same slope. Line d has a slope of 1/2.

9. Example
Line c has a slope of 1/2. If line e is perpendicular to line c, what is its slope? Perpendicular lines have slopes whose product is 1. Line e has a slope of –2.