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:

- 5
*x*+ 3*y*= 18 - -¾
*x*+ 4*y*= 0 - 29 =
*x*+*y*

## Slope intercept form: *y = mx + b*

Examples:

*y*= 18 - 5*x**y = x*- ¼
*x*+ 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

represents the slope of a line*m*represents the y-intercept of a line*b**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 fory, whenx + 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 9*x*. (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.

- -5
*x*+*y*+ 5*x*= 16 + 5*x* - 0 +
*y*= 16 + 5*x* *y*= 16 + 5*x*

## Multiple Step Solving

## Example 3: Multiple Steps

Solve fory, when ½x+ -y= 12

1. Rewrite -*y* as + -1*y*.

½*x* + -1*y* = 12

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

- ½
*x*+ -1*y*- ½*x*= 12 - ½*x* - 0 + -1
*y*= 12 - ½*x* - -1
*y*= 12 - ½*x* - -1
*y*= 12 + - ½*x*

3. Divide everything by -1.

- -1
*y*/-1 = 12/-1 + - ½*x*/-1 *y*= -12 + ½*x*

## Example 4: Multiple Steps

Solve forywhen 8x+ 5y= 40.

1. Subtract 8*x* from both sides of the equal sign.

- 8
*x*+ 5*y*- 8*x*= 40 - 8*x* - 0 + 5
*y*= 40 - 8*x* - 5
*y*= 40 - 8*x*

2. Rewrite -8*x* as + - 8*x*.

5*y* = 40 + - 8*x*

*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 + - 8
*x*/5 *y*= 8 + -8*x*/5

Edited by Anne Marie Helmenstine, Ph.D.