What Is Slope? Rise Over Run Explained

Slope tells you how steep a line is and whether it rises or falls as you move from left to right.

Quick idea

Slope is vertical change divided by horizontal change. Many teachers call this rise over run.

Steps

1. Pick two points on the line.
2. Find the change in y values.
3. Find the change in x values.
4. Divide the change in y by the change in x.

Worked example

Find the slope between the points (1, 2) and (4, 8).

Full solution

Step-by-step walkthrough

Step 1

The y-value changes from 2 to 8, so the rise is 6.

Step 2

The x-value changes from 1 to 4, so the run is 3.

Step 3

Six divided by 3 equals 2.

Common mistake

Keep the same point order in the numerator and denominator. If you start with the second y-value, start with the second x-value too.

Practice problems

1. Find the slope from (0, 1) to (2, 5).
2. Find the slope from (3, 7) to (5, 7).
3. Find the slope from (1, 6) to (4, 0).

Answers

1. 2
2. 0
3. -2

Ask Pennpaper to explain it live

If the steps make sense but you still feel stuck, start a Pennpaper lesson and ask the tutor to draw the problem on the whiteboard. Seeing the symbols move step by step is often what makes the concept click.

Related guides

• How to Graph a Linear Equation
• Slope-Intercept Form Explained
• How to Solve Ratio Problems