The slope intercept form of an equation is y = mx + b, which defines a line. When the line is graphed, m is the slope of the line and b is where the line crosses the y-axis or the y-intercept. You can use slope intercept form to solve for x, y, m, and b
Follow along with these examples to see how to translate linear functions into a graph-friendly format, slope intercept form and how to solve for algebra variables using this type of equation.
Two Formats of Linear Functions
Standard Form: ax + by = c
Examples:
- 5x + 3y = 18
- -¾x + 4y = 0
- 29 = x + y
Slope intercept form: y = mx + b
Examples:
- y = 18 - 5x
- y = x
- ¼x + 3 = y
The primary difference between these two forms is y. In slope intercept form — unlike standard form —y is isolated. If you're interested in graphing a linear function on paper or with a graphing calculator, you'll quickly learn that an isolated y contributes to a frustration-free math experience.
Slope intercept form gets straight to the point:
y = mx + b
- m represents the slope of a line
- b represents the y-intercept of a line
- x and y represent the ordered pairs throughout a line
Learn how to solve for y in linear equations with single and multiple step solving.
Single Step Solving
Example 1: One Step
Solve for y, when x + y = 10.
1. Subtract x from both sides of the equal sign.
- x + y - x = 10 - x
- 0 + y = 10 - x
- y = 10 - x
Note: 10 - x is not 9x. (Why? Review Combining Like Terms.)
Example 2: One Step
Write the following equation in slope intercept form:
-5x + y = 16
In other words, solve for y.
1. Add 5x to both sides of the equal sign.
- -5x + y + 5x = 16 + 5x
- 0 + y = 16 + 5x
- y = 16 + 5x
Multiple Step Solving
Example 3: Multiple Steps
Solve for y, when ½x + -y = 12
1. Rewrite -y as + -1y.
½x + -1y = 12
2. Subtract ½x from both sides of the equal sign.
- ½x + -1y - ½x = 12 - ½x
- 0 + -1y = 12 - ½x
- -1y = 12 - ½x
- -1y = 12 + - ½x
3. Divide everything by -1.
- -1y/-1 = 12/-1 + - ½x/-1
- y = -12 + ½x
Example 4: Multiple Steps
Solve for y when 8x + 5y = 40.
1. Subtract 8x from both sides of the equal sign.
- 8x + 5y - 8x = 40 - 8x
- 0 + 5y = 40 - 8x
- 5y = 40 - 8x
2. Rewrite -8x as + - 8x.
5y = 40 + - 8x
Hint: This is a proactive step toward correct signs. (Positive terms are positive; negative terms, negative.)
3. Divide everything by 5.
- 5y/5 = 40/5 + - 8x/5
- y = 8 + -8x/5
Edited by Anne Marie Helmenstine, Ph.D.