Slope Calculator

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 Slope
• Find Points at a Distance
• Find the Missing x or y

Find the Slope of a Line

Point #1 Coordinates:

x₁

y₁

Point #2 Coordinates:

x₂

y₂

Find Points on a Line at a Distance From Another Point

Point Coordinates:

x₁

y₁

Slope (m)

or

Angle degrees

Distance

Find a Point on a Line Given it's x or y Value

Point #1 Coordinates:

x₁

y₁

Point #2 x or y Coordinate:

x₂

or

y₂

Enter an x or y coordinate for the second point to find the other value

Slope (m)

or

Angle degrees

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Slope:

Slope:

m =

2

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

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Line Graph:

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Slope Intercept Form:

y = 2x + 1

Point Slope Form:

y − 3 = 2(x - 1)

Standard Form:

2x - 1y = -1

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Angle, Distance, & Intercepts:

Angle (θ):	63.435°
Distance:	2.236
Δx:	1
Δy:	2
x-Intercept:	-0.5
y-Intercept:	1

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Steps to Find Slope

Start with the slope formula

m=(y₂ - y₁) / (x₂ - x₁)

Step One: Substitute point values in the formula

m=(5 - 3) / (2 - 1)

Step Two: Simplify the fraction

m=(5 - 3) / (2 - 1)=2 / 1

Step Three: Solve for slope (m)

m=2

Coordinates on the Line:

Right:	(x2, y2)
Left:	(x2, y2)

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Line Graph:

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Slope Intercept Form:

 

Point Slope Form:

 

Standard Form:

 

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Slope, Angle, and Intercepts:

Slope (m):
Angle (θ):
x-Intercept:
y-Intercept:

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Steps to Find Coordinates at a Distance From a Point

Step One: Solve for the right x₂:

right x₂=x₁+d / √(1 + m²)

Step Two: Solve for the right y₂:

right y₂=y₁+m×d / √(1 + m²)

Step Three: Solve for the left x₂:

left x₂=x₁-d / √(1 + m²)

Step Four: Solve for the left y₂:

left y₂=y₁-m×d / √(1 + m²)

Point #2 Coordinates:

(x₂, y₂)

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Line Graph:

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Slope Intercept Form:

 

Point Slope Form:

 

Standard Form:

 

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Angle, Distance, & Intercepts:

x2:
y2:
Slope (m):
Angle (θ):
Distance:
Δx:
Δy:
x-Intercept:
y-Intercept:

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Steps to Find the Missing Coordinate

Start with the slope formula

m=(y₂ - y₁) / (x₂ - x₁)

Step One: Substitute point values in the formula:

Enter the slope, first point coordinates, and the known x or y coordinate into the formula to solve.

Step Two: Simplify the equation:

Simplify the fraction as far as possible.

Step Three: Cross-multiply the fraction and solve:

Cross-multiply the numerators with the opposite denominators and solve.

Learn how we calculated this below

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On this page:

• Slope Calculator
• How to Find the Slope of a Line
• Slope Formula
• Steps to Find Slope Using the Formula
• How to Interpret Slope
• How to Find the Equation of a Line Using the Slope
• How to Find Slope-Intercept Form
• How to Find Point-Slope Form
• How to Find Standard Form
• How to Find the x and y Intercepts of a Line
• How to Find a Point Given 1 Point, Slope, and Distance
• How to Find the Distance Between 2 Points
• Frequently Asked Questions
• References

[ see all ]

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By

Joe Sexton

Joe is the creator of Inch Calculator and has over 20 years of experience in engineering and construction. He holds several degrees and certifications.

Full bio

Reviewed by

Ethan Dederick, PhD

Ethan has a PhD in astrophysics and is currently a satellite imaging scientist. He specializes in math, science, and astrophysics.

Full bio

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Cite As:

Sexton, J. (n.d.). Slope Calculator. Inch Calculator. Retrieved November 17, 2024, from https://www.inchcalculator.com/slope-calculator/

How to Find the Slope of a Line

Slope is a measure of the rate of incline or steepness of a line on a graph. You can find the slope of a line by comparing any 2 points on the line. A point is an x and y value of a cartesian coordinate on a grid.

Slope, expressed as m, is equal to the rise between two coordinates on a line over the run, or rather, it’s the ratio of rise to run.

Rise is the vertical change of the line, or the change in altitude or elevation, and the run is the horizontal change, or the change in distance.^[1] In mathematical terms, on a cartesian coordinate grid, rise is the change in y and run is the change in x.

Slope Formula

You can find the slope m of a line using the following formula:^[2]

m = y₂ – y₁ / x₂ – x₁

Thus, the slope m is equal to y₂ minus y₁, divided by x₂ minus x₁. This is often referred to as the rise over run formula.

Steps to Find Slope Using the Formula

To find the slope of a line using this formula, you’ll need to take any two points along a line and use 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.

Then, follow three easy steps to calculate the slope.

Step One: Substitute Points in the Slope Formula

Start by replacing the y₁, y₂, x₁, and x₂ values in the formula with the coordinates for the two points on the line.

Step Two: Find the Difference in x and y Coordinates

Next, evaluate the numerator and denominator of the slope formula using these values. The absolute value of the numerator will be the vertical distance between the two points, and the absolute value of the denominator will be the horizontal distance between the two points.

The numerator represents the change in the value of y, which is known as the delta of y, or just Δy. You can find the delta of y using the formula:

Δy = y₂ – y₁

The denominator represents the change in the value of x, which is known as the delta of x, or Δx. You can find the delta of x using the formula:

Δx = x₂ – x₁

Step Three: Divide the Delta of y by the Delta of x

The final step is to divide the delta of y by the delta of x to find the slope. You can do this by dividing the numerator in the slope formula by the denominator, or more simply, by using a fraction to decimal calculator.

In some cases, you may want to represent the slope as a fraction or ratio. In this case, you can simplify the fraction to reduce it to its simplest form rather than converting it to a decimal.

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

How to Interpret Slope

While the slope of a line doesn’t tell us where the line is located on the graph, it does tell us the angle of the line.

If the slope is positive, then the line is slanted up and rises from left to right on the graph.

If the slope is negative, then the line is slanted down and drops from left to right on the graph.

If the slope is equal to zero, the line is horizontal and does not slant up or down. This is known as a line with no slope.

In the special case of a vertical line, the slope is undefined. This is because any two points on the line have the same x value, so delta x would equal zero. Therefore, when calculating the slope, one would be dividing by zero, thereby making the slope infinite or undefined.

How to Find the Equation of a Line Using the Slope

Now that you found the slope, you can mathematically express a linear line using one of several equations. The most common equations for a line are slope-intercept form, point-slope form, and standard form.

How to Find Slope-Intercept Form

Slope-intercept form is one of the most commonly used equations to represent a line. You can find the equation of a line using slope-intercept form given the slope m and one point on the line.

Slope-Intercept Form Equation

The slope-intercept form equation is:^[3]

y = mx + b

The slope-intercept form equation states that the y value of a coordinate on the line is equal to the x value of the coordinate times the slope m, plus the y-intercept b.

How to Find Point-Slope Form

Point-slope form is another commonly used equation to represent a line. You can find the equation of a line using point-slope form given the slope m and one point on the line.

Point-Slope Form Equation

The point-slope form equation is:^[4]

y – y₁ = m(x – x₁)

The point-slope form equation states that y minus the y₁ coordinate is equal to the slope m times x minus the x₁ coordinate.

How to Find Standard Form

Standard form is a standardized format for linear equations. To use standard form, the slope and coordinates should be whole numbers; decimal values are generally not used in standard form.

Standard Form Equation

The standard form equation is:

Ax + By = C

Given either of the linear equations above, you can convert to standard form by simply rearranging the equations to isolate the constant C on one half of the equation. If there are any fractions, then multiply both sides of the equation by the denominator of the fractions to remove them.

This formula represents the standard form for linear equations. (Numbers can also be expressed in standard form as well!)

How to Find the x and y Intercepts of a Line

Given the slope of a line and one point on it, you can find the x and y intercepts using one of the linear equations above. The x-intercept is where the line crosses the x-axis, and the y-intercept is where the line crosses the y-axis.

To find these values, start by finding the equation’s slope-intercept form.

Then, given slope-intercept form, you can find the y-intercept by setting x in the equation to 0 and solving for y.

Similarly, to find the x-intercept, set y in the equation to 0 and solve for x.

How to Find a Point Given 1 Point, Slope, and Distance

Points on a line can be found given the slope of the line m and the distance from another point d. Say we have point 1 with the coordinates (x₁, y₁), and we’re trying to find the coordinates (x₂, y₂) of point 2.

The formulas to find x₂ and y₂ if point 2 is to the right of point 1 are:

x₂ = x₁ + d / (1 + m²)

y₂ = y₁ + m × d / (1 + m²)

The formulas to find x₂ and y₂ if point 2 is to the left of point 1 are:

x₂ = x₁ – d / (1 + m²)

y₂ = y₁ – m × d / (1 + m²)

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)

You might also be interested in finding the midpoint or endpoints of a line using one of our calculators.

Frequently Asked Questions

How is finding slope used in real life?

How do you calculate percent slope?

How do you convert an angle to slope?

How do you convert a slope to an angle?

How do you find the slope of a curve?