Slope Intercept Form

What Slope Intercept Form Means and How to Find It

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.

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Two Formats of Linear Functions

Slope intercept form is a way of describing a line as an equation.
Slope intercept form is a way of describing a line as an equation. commerceandculturestock

Standard Form: ax + by = c

Examples:

  • 5x + 3y = 18
  • x + 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.

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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
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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.

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Your Citation
Ledwith, Jennifer. "Slope Intercept Form." ThoughtCo, Nov. 12, 2016, thoughtco.com/slope-intercept-form-2312018. Ledwith, Jennifer. (2016, November 12). Slope Intercept Form. Retrieved from https://www.thoughtco.com/slope-intercept-form-2312018 Ledwith, Jennifer. "Slope Intercept Form." ThoughtCo. https://www.thoughtco.com/slope-intercept-form-2312018 (accessed May 20, 2018).