What Slope-Intercept Form Ways and How to Find It

Updated on March 04, 2019

The gradient-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. Yous tin use slope intercept form to solve for 10, y, 1000, and b. Follow along with these examples to meet how to translate linear functions into a graph-friendly format, slope intercept form and how to solve for algebra variables using this blazon of equation.

Two Formats of Linear Functions

a woman drawing a line with a ruler on a chalk board

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Standard Form: ax + by = c

Examples:

  • 5x + 3y = xviii
  • -¾10 + 4y = 0
  • 29 = x + y

Slope intercept form: y = mx + b

Examples:

  • y = 18 - 5x
  • y = x
  • ¼x + iii = y

The primary difference between these ii forms is y. In slope-intercept form — unlike standard form —y is isolated. If you're interested in graphing a linear office on newspaper or with a graphing reckoner, yous'll quickly learn that an isolated y contributes to a frustration-free math experience.

Gradient intercept form gets straight to the point:


y = chiliad10 + b
  • m represents the gradient 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.

Unmarried Step Solving

Instance 1: One Stride


Solve for y, when 10 + y = x.

1. Subtract x from both sides of the equal sign.

  • x + y - ten = x - x
  • 0 + y = 10 - 10
  • y = 10 - x

Note: ten - 10 is not 9x. (Why? Review Combining Like Terms.)

Example 2: One Stride

Write the following equation in gradient intercept form:


-vx + 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 = xvi + 5x
  • y = sixteen + 5ten

Multiple Pace Solving

Case iii: Multiple Steps


Solve for y, when ½ten + -y = 12

i. Rewrite -y as + -1y.

½x + -1y = 12

2. Subtract ½x from both sides of the equal sign.

  • ½ten + -oney - ½x = 12 - ½x
  • 0 + -1y = 12 - ½x
  • -1y = 12 - ½x
  • -1y = 12 + - ½x

three. Separate everything past -one.

  • -1y/-1 = 12/-one + - ½x/-1
  • y = -12 + ½x

Instance 4: Multiple Steps


Solve for y when eight10 + 5y = 40.

one. Subtract 8x from both sides of the equal sign.

  • 810 + 5y - eightx = 40 - 810
  • 0 + 5y = 40 - eightx
  • fivey = 40 - eight10

2. Rewrite -eightx every bit + - 8ten.

5y = 40 + - 8x

Hint: This is a proactive step toward correct signs. (Positive terms are positive; negative terms, negative.)

3. Carve up everything past 5.

  • 5y/5 = 40/v + - viiix/5
  • y = viii + -8x/5

Edited by Anne Marie Helmenstine, Ph.D.

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