Find the slope through (1, 2) and (4, 8).
- Change in y is 8 − 2 = 6.
- Change in x is 4 − 1 = 3; divide 6 by 3.
Answer: 2
Slope and Rate of Change Worksheets
Connect functions with inputs, outputs, equations, slopes and coordinate graphs.
Learn the skill
Slope as a rate of change
Slope compares the change in output to the change in input. For two points on a nonvertical line, m = (y₂ − y₁)/(x₂ − x₁). A linear relationship has a constant slope.
A method you can use
- Choose two distinct points and label their coordinates consistently.
- Subtract y-values in the same point order as x-values.
- Divide and interpret the sign and units. A zero denominator indicates a vertical line with undefined slope.
Worked examples
Find the slope through (0, 5) and (2, 1).
- Change in y is 1 − 5 = −4.
- Change in x is 2; divide −4 by 2.
Answer: −2
Find the slope through (−1, 3) and (4, 3).
- The y-values do not change: 3 − 3 = 0.
- 0 divided by 5 is 0; the line is horizontal.
Answer: 0
Try it yourself
Solve these before opening the answers. The printable sets below give you more practice.
1. Find the slope through (2, 4) and (5, 10).
Show answer and explanation
2
(10 − 4)/(5 − 2) = 6/3.
2. Find the slope through (1, 7) and (3, 3).
Show answer and explanation
−2
(3 − 7)/(3 − 1) = −4/2.
Before you begin
Read ordered pairs and solve linear equations using signed arithmetic.
Choose your level
These sets use the same exercise types and number ranges across level labels. Choose a fresh set for additional practice.
- Easy: Start with the preview and follow the worked example.
- Medium: Practice the same exercise types with a fresh numbered set.
- Hard: Use another set to practice explaining and checking your answers.
Questions and answer calculations checked on 2026-09-17. How we check worksheets. Free for personal and classroom use.
Preview and print an easy set
Try six questions below, or choose a full set at your level.
1
Find the slope through (0, -1) and (3, 2).
2
Find the slope through (2, 1) and (5, 4).
3
Find the slope through (-2, -1) and (0, 1).
4
Find the slope through (-2, -2) and (2, 6).
5
Find the slope through (2, 3) and (5, 9).
6
Find the slope through (-4, -6) and (-2, -4).
Answer Key
1. 12. 13. 14. 25. 26. 1