Put in Slope Intercept Form Calculator

Slope-intercept form (y = mx + b) is the most common way to represent linear equations in algebra. This calculator helps you convert equations to this standard form quickly and accurately.

What is Slope-Intercept Form?

The slope-intercept form of a linear equation is written as y = mx + b, where:

y is the dependent variable (usually the output)
m is the slope of the line (rate of change)
x is the independent variable (usually the input)
b is the y-intercept (where the line crosses the y-axis)

This form is particularly useful because it clearly shows the slope and y-intercept of the line, making it easy to graph and interpret the equation.

Slope-Intercept Form Formula:

y = mx + b

How to Convert to Slope-Intercept Form

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

Start with the given equation
Solve for y by isolating it on one side of the equation
Express the equation in the form y = mx + b

Example Conversion

Let's convert the equation 2x - 3y = 6 to slope-intercept form:

Start with: 2x - 3y = 6
Subtract 2x from both sides: -3y = -2x + 6
Divide every term by -3: y = (2/3)x - 2

The final slope-intercept form is y = (2/3)x - 2.

Note: The slope (m) is 2/3 and the y-intercept (b) is -2.

Example Calculations

Here are three examples of converting different types of linear equations to slope-intercept form:

Example 1: Standard Form

Convert 4x + 5y = 20 to slope-intercept form.

Start with: 4x + 5y = 20
Subtract 4x from both sides: 5y = -4x + 20
Divide every term by 5: y = (-4/5)x + 4

Result: y = (-4/5)x + 4

Example 2: Point-Slope Form

Convert y - 3 = 2(x - 5) to slope-intercept form.

Start with: y - 3 = 2(x - 5)
Distribute the 2: y - 3 = 2x - 10
Add 3 to both sides: y = 2x - 7

Result: y = 2x - 7

Example 3: Two-Point Form

Convert (y - 2)/(x + 1) = 3 to slope-intercept form.

Start with: (y - 2)/(x + 1) = 3
Multiply both sides by (x + 1): y - 2 = 3(x + 1)
Distribute the 3: y - 2 = 3x + 3
Add 2 to both sides: y = 3x + 5

Result: y = 3x + 5

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, while standard form (Ax + By = C) is more general and doesn't show these values as clearly.
How do I know if an equation is in slope-intercept form?: An equation is in slope-intercept form if it is written as y = mx + b, with y isolated on one side and no other variables on that side.
What does the slope (m) represent in slope-intercept form?: The slope (m) represents the rate of change or steepness of the line. It tells you how much y changes for each unit change in x.
What does the y-intercept (b) represent in slope-intercept form?: The y-intercept (b) represents the point where the line crosses the y-axis. It's the value of y when x = 0.
Can slope-intercept form be used for any linear equation?: Yes, slope-intercept form can be used for any linear equation that can be expressed as a straight line. Non-linear equations cannot be represented in this form.