Grade 9 Linear Relations worksheet
from Gradelings · Name: ______________________
How to explain it
- A line has the equation y = mx + b.
- The slope m is rise ÷ run. The y-intercept b is where the line crosses the y-axis.
- Find the slope from two points on the line.
Example: A line goes through (0, 1) and (2, 5). What is its slope? Rise: 5 − 1 = 4. Run: 2 − 0 = 2. Slope: 4 ÷ 2 = 2. Answer: 2 (so y = 2x + 1)
Question 1
What is the slope of the line through (2, 3) and (5, -3)?
answer box
-2
Hint: slope = rise ÷ run = (-3 − 3) ÷ (5 − 2) = −6 ÷ 3 = −2.
Question 2
Find the slope of the line through (-1, 1) and (4, -3).
- -5/4
- -4/5
- 4/5
- 5/4
-4/5
Hint: rise = −4, run = 5, so slope = -4/5.
Question 3
What is the y-intercept of y = -6x − 7?
answer box
-7
Hint: In y = mx + b, the y-intercept is b. Here b = −7.
Question 4
Which equation has slope −5 and a y-intercept of 4?
- y = -5x + 4
- y = 5x + 4
- y = 4x − 5
- y = -5x − 4
y = -5x + 4
Hint: Use y = mx + b with m = −5 and b = 4: y = -5x + 4.
Question 5
Is the point (5, 22) on the line y = 3x + 5?
- No
- Yes
No
Hint: Substitute x = 5: y = 3(5) + 5 = 20. This is not 22.
Question 6
What is the x-intercept of y = 3x − 24?
answer box
8
Hint: At the x-intercept, y = 0. Solve 3x − 24 = 0, so x = 8.
Question 7
A plant is 11 cm tall and grows 3 cm each week. How tall is it after 6 weeks?
answer boxcm
29 cm
Hint: Height = 3w + 11. For w = 6: 3 × 6 + 11 = 29 cm.
Question 8
The table shows a linear relation. Estimate the cost for 15 hours. This is extrapolation (beyond known values).
Hours (h) Cost ($) 2 16 4 22 6 28 8 34 answer box
55
Hint: The cost rises by 3 per hour, with a start of 10: cost = 3h + 10. For h = 15: 55.
Question 9
Which line is parallel to y = 2x − 2?
- y = 2x − 5
- y = -2x − 2
- y = 3x − 2
- y = 4x − 3
y = 2x − 5
Hint: Parallel lines have the same slope, 2. Only y = 2x − 5 has that slope.
Question 10
In y = mx + b, what does b represent?
- the y-intercept, where the line crosses the y-axis
- the x-intercept
- the slope
- the number of points
the y-intercept, where the line crosses the y-axis
Hint: When x = 0, y = b. That's the point (0, b) on the y-axis.
Answer key
- 1. -2
- 2. -4/5
- 3. -7
- 4. y = -5x + 4
- 5. No
- 6. 8
- 7. 29 cm
- 8. 55
- 9. y = 2x − 5
- 10. the y-intercept, where the line crosses the y-axis
Want more than 10 questions?
In Gradelings the questions change every time and adjust to your child, with hints and kind feedback.