Slope Intercept Form Calculator

Slope intercept form: y = mx + b

The slope intercept form calculator tells you how to find the equation of a line for any given two points that this line passes through. It will help you find the coefficients of slope and y-intercept, as well as the x-intercept, using the slope intercept formulas. Read on to learn what is the slope intercept form of a linear equation.

What is the slope intercept form

Linear equations, or straight line equations, can be recognized by having no terms with exponents on them. (For example, you will find an x or a y, but never an .) Each linear equation describes a straight line.

You can present the equation of any line in the form of y = mx + b. This is the so-called slope intercept form, because it gives you two important informations: about the slope m and the y-intercept b of the line. You can use these values for linear interpolation later.

Slope is the inclination, or gradient, of a line. If it is positive, the values of y increase with increasing x; if it is negative, y decreases with an increasing x. You can read more about it in the description of our slope calculator.

Y-intercept is the value of y at which the line crosses the y-axis. To find it, you have to substitute an x = 0 to the linear equation.

Slope intercept formula derivation

How to find the slope intercept form of a linear equation, then? We will assume you know two points that the straight line goes through. The first one will have coordinates (x₁, y₁) and the second one (x₂, y₂). Your unknowns are the slope m and the y-intercept b.

Firstly, substitute the coordinates of the two points into the slope intercept equation:

(1) y₁ = mx₁ + b

(2) y₂ = mx₂ + b

Then, subtract the first equation from the second:

y₂ - y₁ = m(x₂ - x₁)

Finally, divide both sides of the equation by (x₂ - x₁) to find the slope:

m = (y₂ - y₁)/(x₂ - x₁)

Once you have found the slope, you can substitute it into the first or second equation to find the y-intercept:

y₁ = x₁(y₂ - y₁)/(x₂ - x₁) + b

b = y₁ - x₁(y₂ - y₁)/(x₂ - x₁)

How to find the equation of a line

This slope intercept form calculator allows you to find the equation of a line in the slope intercept form, if all you have given are two points that the line goes through. You need to follow the procedure outlined below.

  1. Write down the coordinates of the first point. Let's assume it is a point with x₁ = 1 and y₁ = 1.
  2. Write down the coordinates of the second point as well. Let's take a point with x₂ = 2 and y₂ = 3.
  3. Use the slope intercept formula to find the slope: m = (y₂ - y₁)/(x₂ - x₁) = (3-1)/(2-1) = 2/1 = 2.
  4. Calculate the y-intercept: b = y₁ - m * x₁ = 1 - 2*1 = -1. You can also use x₂ and y₂ instead of x₁ and y₂ here.
  5. Put all these values together to construct the slope intercept form of a linear equation: y = 2x - 1.
  6. You can also use the distance calculator to find the distance between the two points.

x-intercept and y-intercept

You can also find the x-intercept of the line. It is the value of x at which the straight line crosses the x-axis (it means the value of x for which y = 0). You can calculate it in the following way:

0 = mx + b

x = -b/m

Our slope intercept calculator will display the values of x-intercept and y-intercept for you.