What Slope-Intercept Form Ways and How to Observe It

Updated on March 04, 2019

The slope-intercept class of an equation is y = mx + b, which defines a line. When the line is graphed, m is the gradient of the line and b is where the line crosses the y-axis or the y-intercept. You tin can use slope intercept grade to solve for x, y, m, and b. Follow forth with these examples to see how to interpret linear functions into a graph-friendly format, gradient intercept form and how to solve for algebra variables using this type 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 = eighteen
  • -¾10 + 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 ii forms is y. In slope-intercept form — unlike standard form —y is isolated. If you lot're interested in graphing a linear office on paper or with a graphing estimator, you'll quickly learn that an isolated y contributes to a frustration-gratuitous math experience.

Gradient intercept form gets direct to the point:


y = chiliadx + 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 Footstep Solving

Example 1: One Step


Solve for y, when x + y = 10.

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

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

Note: x - x is not ninex. (Why? Review Combining Like Terms.)

Example 2: One Pace

Write the following equation in slope intercept form:


-fivex + y = 16

In other words, solve for y.

ane. Add together 5x to both sides of the equal sign.

  • -vten + y + 5x = 16 + 5x
  • 0 + y = 16 + 5ten
  • y = 16 + 510

Multiple Stride Solving

Example iii: 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.

  • ½ten + -iy - ½x = 12 - ½ten
  • 0 + -1y = 12 - ½10
  • -1y = 12 - ½x
  • -aney = 12 + - ½10

3. Divide everything by -i.

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

Instance four: Multiple Steps


Solve for y when 8x + fivey = 40.

1. Subtract eight10 from both sides of the equal sign.

  • viiix + 5y - eightx = twoscore - 8x
  • 0 + 5y = twoscore - 8x
  • vy = forty - 8x

ii. Rewrite -8x every bit + - eightx.

5y = 40 + - eightx

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

iii. Divide everything by v.

  • 5y/5 = 40/5 + - 8x/5
  • y = eight + -8x/five

Edited by Anne Marie Helmenstine, Ph.D.

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