A free printable linear relations worksheet for Grade 8 math.
By Kris Reddy, Ontario teacher · Updated October 16, 2026 · 22 questions (30 marks) · PDF + answer key
This free linear relationships worksheet helps Grade 8 students connect the three ways of showing a linear relation: a table of values, a rule and a graph. Students complete tables from a rule, find the rule from a table, decide which tables are linear, and solve three real-world problems about a plumber's bill, a burning candle and a filling pool.
On the second page they graph two relations on blank grids, write the rule for two drawn lines, extend a growing tile pattern into a rule, and correct two common mistakes. Every answer in the key shows the working and was checked by computer, and the key includes the finished graphs. To print it, use the Download button above.
| Part | Skill practised | Marks |
|---|---|---|
| A | Complete tables of values from a rule | 4 |
| B | Find the rule from a table | 4 |
| C | Linear or not? (constant differences) | 2 |
| D | Three real-world problems | 6 |
| E | Graph two relations on blank grids | 4 |
| F | Find the rule from a drawn graph | 4 |
| G | Growing tile pattern | 4 |
| H | Spot the mistake | 2 |
The linear relationships worksheet supports the Ontario Grade 8 math curriculum in the Algebra strand, where students describe and compare linear relations using tables of values, graphs and equations, and use them to make predictions.
A relation is linear when y changes by the same amount every time x goes up by 1. That steady change is called the constant difference, or rate of change. Because the change never speeds up or slows down, the points on its graph line up in a straight line.
| x | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
| y | 1 | 2 | 4 | 8 |
The table above is not linear: the differences are +1, +2 and +4, so the graph would curve upward. Part C of the linear relationships worksheet asks students to spot this by checking the differences.
Every linear rule has two parts: what you multiply x by, and what you add. Find them straight from the table:
| x | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
| y | 4 | 7 | 10 | 13 |
If y goes down, the multiplier is negative. For 10, 8, 6, 4 the rule is y = −2x + 10. Part B of the linear relationships worksheet includes one rule with a negative multiplier, one with nothing added and one that subtracts.
To graph a rule, make a table of values, plot each (x, y) point, and join them with a ruler. Here is y = 3x + 4:
Reading a graph works backwards: count how far the line rises for each step to the right, then read where it crosses the y-axis. That's exactly what Part F of the linear relationships worksheet asks. To brush up on the algebra behind it, see the two-step equations worksheet, or read more about linear functions on Wikipedia.
A pattern that grows by the same number of tiles each time is a linear relation in disguise.
This pattern has 3, 5 and 7 tiles, adding 2 each time, so the rule is t = 2n + 1. In Part G of the linear relationships worksheet, students use the rule to work out which figure has 31 tiles. Spotting the "add 2" and the "+ 1" is the same skill as finding a rule from a table.
These questions match the linear relationships worksheet PDF, which has tables to fill in, coordinate grids and drawn graphs.
Open each part to check the linear relationships worksheet answers. The printable key, with the finished graphs, is on the last two pages of the PDF.
These are the errors that come up most when marking this linear relationships worksheet. Part H targets two of them directly.
For more practice, try the algebra basics quiz and the multi-step word problems quiz.
Yes. The worksheet and its answer key are free to download and print as one PDF, with no account needed.
A linear relationship is one where y changes by the same amount every time x goes up by 1. Its table has a constant difference, and its graph is a straight line.
Find how much y changes each time x goes up by 1; that number multiplies x. Then find y when x = 0; that number is added on. For y = 4, 7, 10, 13 starting at x = 0, the rule is y = 3x + 4.
Subtract each y-value from the next one. If the differences are all the same, the relation is linear. 1, 2, 4, 8 is not linear because the differences are 1, 2 and 4.
It is written for Grade 8 math and works well as Grade 9 review before slope and y = mx + b.
Ready to start? Use the Download button above to print the free linear relationships worksheet double-sided, and keep the answer key pages for marking.