# Slope Calculator – Find the Slope of a Line

Use the slope calculator to find the slope of a line that passes through 2 points or solve a coordinate given *m*. Plus, the calculator will also solve 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

## 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

### Steps to Find Slope

_{2}- y

_{1}) / (x

_{2}- x

_{1})

## On this page:

- Slope Calculator
- How to Find the Slope of a Line Given 2 Points
- The Slope Formula
- Use the Formula to Find Slope
- How to Find Slope-Intercept Form
- Slope-Intercept Form Equation
- How to Find a Point Given 1 Point, Slope, and Distance
- How to Convert Slope to Angle
- How to Convert Angle to Slope
- How to Find the Distance Between 2 Points
- How to Solve the Delta of x and y

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

Slope is the angle of a line on a graph. It 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 *m* is equal to the rise between two coordinates on a line over the run. Rise is the vertical increase of the line, and run is the horizontal increase.

### The Slope Formula

Slope, represented as *m*, can be found using the following formula:

slope = y_{2} – y_{1} / x_{2} – x_{1}

Thus, the slope *m* is equal to *y _{2}* minus

*y*, divided by

_{1}*x*minus

_{2}*x*.

_{1}### Use the Formula to Find Slope

To find the slope of a line, start by finding 2 points along a line and find their *x* and *y* values. The value of *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.

**For example**, let’s find the slope of a line that passes through the points (3,2) and (7,5).

Start with the slope formula:

m = (y_{2} – y_{1}) / (x_{2} – x_{1})

Replace the *x* and *y* values with the coordinate’s *x* and *y* values, then solve.

m = 5 – 2 / 7 – 3

m = 3 / 4

Thus, the slope *m* is equal to 3 / 4

The slope formula is useful for points along a linear line, but when working with non-linear functions you might need to use an average rate of change calculator.

## How to Find Slope-Intercept Form

A linear line can be expressed using slope-intercept form, which is an equation representing the line. Slope-intercept form can be solved using *m* and one point on the line.

### Slope-Intercept Form Equation

The equation of a linear line can be expressed using the following equation, where *m* is the slope of the line, and *b* is the y-intercept value.

y = mx + b

Thus, the equation representing a line using slope-intercept form is the *y* value of a coordinate on the line is equal to the *x* value of the coordinate times *m*, plus the y-intercept *b*.

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

Substitute for m:

y = 1 / 2 × x + b

Substitute the point values for x and y:

4 = 1 / 2 × 5 + b

Solve for b:

4 = 2.5 + b

4 – 2.5 = b

1.5 = b

Substitute *b* in the equation to find the slope-intercept form:

y = 1 / 2x + 1.5

## How to 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:

x_{2} = x_{1} + d / (1 + m^{2})

y_{2} = y_{1} + m × d / (1 + m^{2})

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

x_{2} = x_{1} + -d / (1 + m^{2})

y_{2} = y_{1} + m × -d / (1 + 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 m = 5, then the angle in degrees is tan^{-1}(5).

Our rise and run to degrees converter can help calculate the value in degrees given the rise and run of a line.

## How to Convert Angle to Slope

It’s also possible to convert an angle in degrees to slop, which is equal to the tangent of the angle.

m = tan(θ)

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

## How to Find the Distance Between 2 Points

The formula to find the distance *d* between two points on a line 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 two 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}