# 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:

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degrees

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degrees

## Slope, Angle, & Distance:

Slope:
2
The slope of the line connecting (1, 3) and (2, 5) is 2

Slope (m): 2 63.4349° 2.2361 1 2
Slope Intercept Form:
(y = mx + b)
y = 2x + 1

### Steps to Find Slope

m=(y2 - y1)(x2 - x1)
Substitute point values in the formula
m=(5 - 3)(2 - 1)
Simplify each side of the equation
m=(5 - 3)(2 - 1)=21
Solve for slope (m)
m=2

## 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 = y2 – y1x2 – x1

Thus, the slope m is equal to y2 minus y1, divided by x2 minus x1. ### 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).

m = (y2 – y1)(x2 – x1)

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

m = 5 – 27 – 3
m = 34

Thus, the slope m is equal to 34 ## 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 = 12 × x + b

Substitute the point values for x and y:

4 = 12 × 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 = 12x + 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:

x2 = x1 + d(1 + m2)

y2 = y1 + m × d(1 + m2)

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

x2 = x1 + -d(1 + m2)

y2 = y1 + m × -d(1 + m2)

## 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 = √((x2 – x1)2 + (y2 – y1)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 = x2 – x1

The delta of y can be solved using the formula:

Δy = y2 – y1 