Grade 7 Linear Relations worksheet
from Gradelings · Name: ______________________
How to explain it
- 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
Question 1
What is the value of 7n − 2 when n = 7?
7n − 2
answer box
47
Hint: Replace n with 7: 7 × 7 − 2 = 49 − 2 = 47.
Question 2
Which expression gives the value for any term number n?
n 1 2 3 4 value 1 7 13 19 - 6n − 4
- -6n − 5
- n + 1
- 6n − 5
6n − 5
Hint: The value changes by 6 each time n goes up by 1, so the rule starts with 6n. At n = 1, 6n is 6 but the table shows 1, so subtract 5: 6n − 5.
Question 3
Which point is on the graph of y = 2x + 4?
y = 2x + 4
- (-3, -2)
- (-2, -3)
- (-2, -4)
- (-3, 2)
(-3, -2)
Hint: Substitute each x into the rule and see if you get the y. For x = -3: y = 2 × (-3) + 4 = -2, so (-3, -2) is on the line.
Question 4
Which equation matches the points on the graph?
- y = 3x
- y = -2x
- y = 2x + 1
- y = 2x
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
A bike rental costs $24 plus $4 for each hour. What is the cost, in dollars, for 11 hours?
answer box
68
Hint: Start amount + rate × number: 24 + 4 × 11 = 24 + 44 = 68.
Question 6
This pattern keeps growing the same way. How many chairs are in Figure 36?
Figure 1: 6 chairs
Figure 2: 9 chairs
Figure 3: 12 chairs
Figure 4: 15 chairs
answer box
111
Hint: Each figure adds 3 chairs, so the rule is 3n + 3 for figure n. Figure 36: 3 × 36 + 3 = 111.
Question 7
The equation H = 4w + 19 gives a plant's height H, in centimetres, after w weeks. What does the 19 tell you?
H = 4w + 19
- The number of weeks
- The plant's height at the start
- How much the plant grows each week
- The plant's height
The plant's height at the start
Hint: The number multiplied by the variable (4) is the rate: it's added again for every week. The number added on its own (19) is the starting amount.
Question 8
The table follows a pattern. What number belongs where the ? is?
x 1 2 3 4 8 y 14 16 18 20 ? answer box
28
Hint: Each time x goes up by 1, y changes by 2, so y changes by 2 for each 1 in x. The rule is y = 2x + 12. When x = 8: 2 × 8 + 12 = 28.
Question 9
A bike rental costs $12 plus $7 for each hour. What is the cost, in dollars, for 7 hours?
answer box
61
Hint: Start amount + rate × number: 12 + 7 × 7 = 12 + 49 = 61.
Question 10
Which point is on the graph of y = x + 3?
y = x + 3
- (5, 2)
- (-2, 5)
- (2, -5)
- (2, 5)
(2, 5)
Hint: Substitute each x into the rule and see if you get the y. For x = 2: y = 1 × 2 + 3 = 5, so (2, 5) is on the line.
Answer key
- 1. 47
- 2. 6n − 5
- 3. (-3, -2)
- 4. y = 2x
- 5. 68
- 6. 111
- 7. The plant's height at the start
- 8. 28
- 9. 61
- 10. (2, 5)
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