Slope Calculator

Use this slope calculator and let it find the slope (m) or gradient between two points \(A\left(x_1, y_1\right)\) and \(B\left(x_2, y_2\right)\) in the Cartesian coordinate plane. Also, you can use the slope finder to calculate the following parameters: 

• Slope intercept form
• Grade, distance, and angle
• ?Y and X−coordinates
• Slope graph
• The x-intercept
• The y-intercept

What Is Slope?

“The slope or gradient of the line is said to be a number that defines both the direction and steepness, incline or grade of line.” Typically, it is denoted by the letter (m) and is mostly known as rise over run.

Slope Formula:

Calculate slope by using the following formula: \(\ Slope \left(m\right)=\tan\theta = \dfrac {y_2 – y_1} {x_2 – x_1}\)

Where

• \(\ m\ is\ the\ slope\)
• \(\theta\ is\ angle\ of\ incline\)

What Are The 4 Different Types of Slopes?

There are four types of slopes depending on the relationship between the two variables (x and y), which are:

• Positive
• Negative
• Zero
• Undefined

In the following slope table we have defined the types for a good understanding:

How To Find Slope of A Line?

To find the slope, use this formula: \(\ Slope \left(m\right)=\tan\theta = \dfrac {y_2 – y_1} {x_2 – x_1}\)

Also, you can use slope of a line formula to make instant calculations:  \(\ y =\ mx + \ b\)

You can expand the above formula to get the line equations in the point slope form: \(\ y - y_{1} =\ m\ (x - x1)\)

Example:

There are two points are given: (2, 1) and (4, 7). We need to find the slope of the line passing through the points, the distance between points, and the angle of inclination. 

Solution:

Given that:

• \(\ x_{1} = 2\)
• \(\ y_{1} = 1\)
• \(\ x_{2} = 4\)
• \(\ y_{2} = 7\)

Put the above values into the slope equation:

\(\ m =\dfrac {y_2 – y_1}{x_2 – x_1} =\dfrac {7 – 1} {4 – 2} =\dfrac {6}{2} = 3\)

Distance Between Two Points:

Use the Pythagorean theorem to find the distance between the points:

\(\ d = \sqrt{{(x_2 - x_1)^2 + (y_2 - y_1)^2}}\)

Substituting the coordinates (2, 1) and (4, 7): \(\ d = \sqrt{{(4 - 2)^2 + (7 - 1)^2}} = \sqrt{{2^2 + 6^2}} = \sqrt{{4 + 36}} = \sqrt{40} \)

Angle of Inclination:

\(\ \tan(\theta) = \dfrac{{y_2 - y_1}}{{x_2 - x_1}}\)

Put the values of coordinates (2, 1) and (4, 7) in the equation above:

\(\ \tan(\theta) = \dfrac{{7 - 1}}{{4 - 2}} = \dfrac{6}{2} = 3 \)

Taking the arctangent (\(\arctan\)) of both sides:  \(\theta = \arctan(3) = 71.56 \ deg\)

FAQ’s:

What Are 3 Ways To Find Slope?

The three ways to calculate slope are:

• Point slope form
• Slope-intercept form
• The standard form

How Do You Convert An Angle To A Slope?

Take the tangent of the angle: \(\ m =\ tan\theta\)