Enter the coordinates of two points into the calculator to determine the slope intercept form of the line between those two points.

## What is slope intercept form?

Slope intercept form gets it’s name from a form of an equation that describes a line. This equation is represented by 4 variables, y,x,m and b. Y and X being coordinate points, m being the slope, and b being the y-intercept of the line. This yields the equation y=mx+b.

This is the most common form of a straight line that’s depicted in the x-y coordinate plane. This equation will not accurately represent other types of lines, such as exponential or hyperbole.

## Slope Intercept Form Calculator

The following is the equation for the slope intercept form:

y = mx + b

- Where y is the y-coordinate
- x is the x-coordinate
- m is the slope
- and b is the y-intercept

From the equation above, the slope (m), can be calculated with the following formula.

slope = (y₂ – y₁) / (x₂ – x₁)

- y₂ = y coordinate of point 2
- y₁ = y coordinate of point 1
- x₂ = x coordinate of point 2
- x₁ = x coordinate of point 1

The y-intercept, b, can be calculated by re-arranging the formula above.

b = y – mx

## How to calculate the slope intercept form of a line

The below example is a step by step guide on how to determine the slope intercept form of line given the coordinates of two points along that line.

- First, we need to determine the x and y coordinates of both points. For this example we will assume those points are (5,6) and (10,20).
- Next, the slope of the line needs to be calculated. This can be done using the formula of slope = (y₂ – y₁) / (x₂ – x₁) , so (20-6)/(10-5)= m = 2.8
- The next step is to determine the y-intercept, b. To do this be simply re-arrange the original equation as done previously to find b = y – mx. = 6 – 2.8*5 = -8.
- Finally, enter the slope and intercept into the slope intercept form equation and we yield y=2.8*x -8
- Analyze the results and apply to future problems.