Grade 7 · Math · Unit 8 of 20
Linear Relations
Patterns in tables and graphs
What your child practises
Finding the rule behind growing patterns, writing expressions like 3n + 2, and connecting tables, graphs and real situations such as rental costs.
Ontario Curriculum expectation: C1.1–C1.3 · linear relations, tables and graphs
How we explain it
Children can open this short lesson before they practise.
- A table pairs each x with a y.
- Look for how y changes each time x goes up by 1.
- Use that change to carry the pattern on.
Example: x = 1, 2, 3 gives y = 5, 8, 11. What is y when x = 4? y goes up by 3 each time. 11 + 3 = 14. Answer: 14
Sample questions
A taste of this unit. In the app, questions change every time and get easier or harder to match your child.
Question 1
The table follows a pattern. What number belongs where the ? is?
x 1 2 3 4 8 y 12 17 22 27 ? answer box
Show answer
47
Hint: Each time x goes up by 1, y changes by 5, so y changes by 5 for each 1 in x. The rule is y = 5x + 7. When x = 8: 5 × 8 + 7 = 47.
Question 2
A tank holds 14 L of water and is being filled at 7 L per minute. How many litres are in the tank after 7 minutes?
answer box
Show answer
63
Hint: Start amount + rate × number: 14 + 7 × 7 = 14 + 49 = 63.
Question 3
Which expression gives the value for any term number n?
n 1 2 3 4 value 8 11 14 17 - 3n + 5
- 8n
- 3n + 6
- 4n + 5
Show answer
3n + 5
Hint: The value changes by 3 each time n goes up by 1, so the rule starts with 3n. At n = 1, 3n is 3 but the table shows 8, so add 5: 3n + 5.
Question 4
Which equation matches the points on the graph?
- y = x + 2
- y = 2x + 2
- y = 3x
- y = 2x
Show answer
y = 2x
Hint: At x = 0 the point is at y = 0. Each step right, y goes up 2. So y = 2x. Check another point: x = 1 gives y = 2.
Question 5
The equation H = 7w + 31 gives a plant's height H, in centimetres, after w weeks. What does the 31 tell you?
H = 7w + 31
- The plant's height
- The plant's height at the start
- The number of weeks
- How much the plant grows each week
Show answer
The plant's height at the start
Hint: The number multiplied by the variable (7) is the rate: it's added again for every week. The number added on its own (31) is the starting amount.
Question 6
Which point is on the graph of y = -3x + 4?
y = -3x + 4
- (2, 1)
- (1, -1)
- (-1, 1)
- (1, 1)
Show answer
(1, 1)
Hint: Substitute each x into the rule and see if you get the y. For x = 1: y = -3 × 1 + 4 = 1, so (1, 1) is on the line.