Slope Calculator

Use this calculator to help you quickly determine the slope of a line. Enter the coordinates for two points to get started.

Point A

(x_{1}, y_{1})

Point B

(x_{2}, y_{2})

Slope m = \frac{- 2}{3}

Slope = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{- 3 - 5}{7 - (- 5)} = \frac{- 8}{12} = \frac{- 2}{3}

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Knowing how to find the slope is an important math concept to understand!

Take a look at these examples to see how it’s done:

Find the Slope from Two Points

💡 Find the slope of a line that passes through the points \((2,3)\) and \((-1,-6)\).

A Cartesian plane showing a line passing through points A (2, 3) and B (−1, −6), with both points marked by yellow dots.

To find the slope from two points, we use the slope formula:

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

First, let’s label the points.

\((x_1,y_1)=(2,3)\)
\((x_2,y_2)=(-1,-6)\)

Now we can plug these into the formula:

\(m=\dfrac{-6-3}{-1-2}\)

Next, simplify the numerator and denominator:

\(m=\dfrac{-9}{-3}\)

The last step is to divide. Keep in mind that a negative divided by a negative is a positive!

\(m=\dfrac{-9}{-3}=\dfrac{3}{1}=3\)

Find the Slope from a Graph

💡 Find the slope of the line shown in the graph below.

Line graph with a positive slope displayed on a grid with x and y axes ranging from -2 to 6.

To find the slope from this graph, we can use “rise over run.”

\(m=\dfrac{\text{rise}}{\text{run}}\)

First, identify two points on the line where the grid lines intersect clearly. Let’s use the points \((0,1)\) and \((3,3)\).

A Cartesian plane showing a line passing through points A (0, 1) and B (3, 3), with both points marked by yellow dots.

Next, we need to count the vertical change (the rise). To get from Point A to Point B, we have to move up two units, which means the rise is positive.

Then, we need to count the horizontal change (the run). To get from Point A to Point B, we have to move right three units, which means the run is also positive.

Rise = 2
Run = 3

All we have to do now is put our rise and run into the formula:

\(m=\dfrac{2}{3} \approx 0.667\)

Find the Slope from an Equation

💡 Find the slope of the line represented by the equation \(4x+2y=8\).

To find the slope from this equation, we need to rewrite it in slope-intercept form, which is \(y=mx+b\).

The variable \(m\) will be the slope, and our goal is to solve the equation for \(y\).

First, we need to subtract \(4x\) from both sides of the equation:

\(2y=-4x+8\)

Then, we need to divide every term by 2 to get \(y\) by itself:

\(\dfrac{2y}{2}=\dfrac{-4x}{2}+\dfrac{8}{2}\)

\(y=-2x +4\)

Now that the equation is in slope-intercept form, we can easily identify the slope, \(m\). It’s the number being multiplied by \(x\), which is –2 in this case.

More Resources

Click below to watch a comprehensive video about finding the slope, along with other helpful resources to help you fully grasp the topic!

Learn More About Slope!