Slope Calculator – Find the Angle or Equation of a Line

Use the slope calculator to do the following:

  • 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

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degrees

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

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degrees

Points, Slope, Angle, & Distance:

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

Slope (m):2
Angle (θ):63.4349°
Distance:2.2361
Δx:1
Δy:2
Slope Intercept Form:
(y = mx + b)
y = 2x + 1

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


Line on a graph connecting two points

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:

Slope (m)=(y2 – y1)(x2 – x1)

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.

For example, for a line that passes through the points (7,3) and (12,7) the formula to find slope would look like this:

m=(7 – 3)(12 – 7)

To solve:

m=45

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. The slope intercept form can be solved using the slope 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 the slope for m:

y=12x+b

Substitute the point values for x and y:

4=12×5+b

Solve for b:

4=2.5+b
4b=2.5
-b=2.54
-b=-1.5
b=1.5

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

y=12x+1.5

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+d1 + m2
y2=y1+m×d1 + m2

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

x2=x1+-d1 + m2
y2=y1+m×-d1 + 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 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 = √((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 2 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