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Put The Following Equation in Slope Intercept Form Calculator

Reviewed by Calculator Editorial Team

This calculator converts linear equations to slope-intercept form (y = mx + b). Slope-intercept form is the most common way to represent linear equations, where m is the slope and b is the y-intercept.

What is Slope-Intercept Form?

The slope-intercept form of a linear equation is written as:

y = mx + b

  • y is the dependent variable (usually represents the output)
  • m is the slope (rate of change)
  • x is the independent variable (usually represents the input)
  • b is the y-intercept (the value of y when x = 0)

This form is particularly useful because it clearly shows the slope and y-intercept of the line, which helps in graphing and understanding the relationship between variables.

How to Convert to Slope-Intercept Form

To convert any linear equation to slope-intercept form, follow these steps:

  1. Start with the given equation
  2. Solve for y in terms of x
  3. Simplify the equation to the form y = mx + b

Tip: Always check your work by plugging in a value for x and verifying that both sides of the equation are equal.

Common Conversion Examples

Original Equation Steps to Convert Slope-Intercept Form
2x + 3y = 6 Subtract 2x from both sides, then divide by 3 y = -⅔x + 2
y - 5 = 3(x + 2) Distribute 3, then add 5 to both sides y = 3x + 11
4y = 2x - 8 Divide all terms by 4 y = ½x - 2

Examples

Example 1: Simple Conversion

Convert 3x - 2y = 4 to slope-intercept form.

  1. Start with: 3x - 2y = 4
  2. Subtract 3x from both sides: -2y = -3x + 4
  3. Divide all terms by -2: y = (3/2)x - 2

The slope-intercept form is y = 1.5x - 2.

Example 2: More Complex Equation

Convert 2(3y - x) = 6 to slope-intercept form.

  1. Start with: 2(3y - x) = 6
  2. Distribute the 2: 6y - 2x = 6
  3. Add 2x to both sides: 6y = 2x + 6
  4. Divide all terms by 6: y = (1/3)x + 1

The slope-intercept form is y = ⅓x + 1.

FAQ

What is the difference between slope-intercept form and standard form?
Slope-intercept form (y = mx + b) shows the slope and y-intercept directly. Standard form (Ax + By = C) shows the coefficients of x and y first.
How do I know if an equation is linear?
A linear equation has variables raised to the first power and no products or squares of variables. It can be written in the form y = mx + b.
What does the slope represent in slope-intercept form?
The slope (m) represents the rate of change of y with respect to x. It tells you how much y changes when x increases by 1.