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.