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.
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:
(y = mx + b)
y = 2x + 1
Steps to Find Slope
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 = y2 – y1 / x2 – 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).
Start with the slope formula:
m = (y2 – y1) / (x2 – x1)
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:
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