# Slope Calculator – Find the Equation of a Line

- Calculate the slope of a line that passes through 2 points
- Solve a coordinate given the slope and distance from a point
- Find the x or y of a point given another point and the slope
- Find the slope intercept form of a line.

**Calculate Using the Following:**

## Find the Slope Given 2 Points

## Find a Point Given 1 Point, Slope, and Distance

## Find a Point Given 1 Point, Slope, and an x or y Value

## Points, Slope, Angle, & Distance:

**2**

Slope (m): | 2 |
---|---|

Angle (θ): | 63.4349° |

Distance: | 2.2361 |

Δx: | 1 |

Δy: | 2 |

**Slope Intercept Form:**

(y = mx + b)

y = 2x + 1

_{2}- y

_{1})(x

_{2}- x

_{1})

## On this page:

## How to Find Slope of a Line Given 2 Points

Slope is the angle of a line on a graph and can be found by comparing any 2 points on the line. A point is an x and y value of a cartesian coordinate on a grid. Slope, often represented as m, can be found using the following formula:

_{2}– y

_{1})(x

_{2}– x

_{1})

To find slope, start by finding x and y values of 2 different points along the line. x is the horizontal distance of the point from the vertical y axis and y is the vertical distance of the point from the horizontal x axis.

The slope (m) is equal to the rise over the run.

Rise is the amount of vertical increase of the line, and can be found by subtracting y_{1} from y_{2}.

Run is the amount of horizontal increase of the line, and can be found by subtracting x_{1} from x_{2}.

**For example**, for a line that passes through the points (3,2) and (7,5) the formula to find slope would look like this:

To solve:

## Using Slope Intercept Form

A linear line can be expressed using the slope intercept form, which is an equation representing the line. The equation of a linear line can be expressed using the formula y = mx + b where m is the slope of the line and b is the y-intercept value. Slope intercept form can be solved using the slope (m) of a line and one point on the line.

**For example**, given a slope of 1/2 and a point (5,4), solve for b.

Substitute for m:

Substitute the point values for x and y:

Solve for b:

Substitute b in the equation to get the slope intercept form:

## Find a Point Given 1 Point, Slope, and Distance

Points on a line can be solved given the slope of the line and the distance from another point. The formulas to find x and y of the point to the right of the point are:

_{2}=x

_{1}+d1 + m

^{2}

_{2}=y

_{1}+m×d1 + m

^{2}

The formulas to find x and y of the point to the left of the point are:

_{2}=x

_{1}+-d1 + m

^{2}

_{2}=y

_{1}+m×-d1 + m

^{2}

## How to Convert Slope to Angle

The angle of a line in degrees can be found from the inverse tangent of the slope (m).

θ = tan^{-1}(m)

**For example**, if slope = 5, then the angle in degrees is tan^{-1}(5).

Our angle unit conversion calculator can help convert the angle measurement from degrees to radians or grad.

## How to Convert Angle to Slope

An angle in degrees can also be converted to a slope. Slope is equal to the tangent of the angle.

m = tan(θ)

**For example**, if angle = 72, then the slope is equal to tan(72).

## How to Find the Distance Between 2 Points

The formula to find the distance (d) between 2 different points is:

d = √((x_{2} – x_{1})^{2} + (y_{2} – y_{1})^{2})

## How to Solve the Delta of x and y

The delta of x and y, expressed using the symbol Δ, is simply the absolute value of the distance between the x values or y values of 2 points.

The delta of x can be solved using the formula:

Δx = x_{2} – x_{1}

The delta of y can be solved using the formula:

Δy = y_{2} – y_{1}

## Infographics

Feel free to use and share our infographics demonstrating the techniques shown above.