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Coordinates

x₁

y₁

x₂

y₂

Slope intercept form: y = mx + b

m

b

Intercepts

x-intercept

y-intercept

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.

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 **x²**.) 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.

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)`

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.

- Write down the coordinates of the first point. Let's assume it is a point with x₁ = 1 and y₁ = 1.
- Write down the coordinates of the second point as well. Let's take a point with x₂ = 2 and y₂ = 3.
- Use the slope intercept formula to find the slope:
`m = (y₂ - y₁)/(x₂ - x₁) = (3-1)/(2-1) = 2/1 = 2`

. - 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. - Put all these values together to construct the slope intercept form of a linear equation:
`y = 2x - 1`

. - You can also use the distance calculator to find the distance between the two points.

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.