WorksheetMint

Grade 7–9Common Core (CCSS) · Math: algebra

Linear Functions y = kx + m — Worksheets with Answers

Practise straight lines with new numbers every time: values, slope, points on the line and the full equation.

Customize worksheet ↓
More options

Linear functions y = kx + m · 14-16 years

Name: ____________________

Worked example

  1. The goal: read or calculate k (slope), m (intercept) or y for a given x.
  2. A linear function looks like y = kx + m. k is the slope, m is where the line crosses the y-axis.
  3. Example: y = 2x + 1. What is y when x = 3? Substitute: y = 2 × 3 + 1 = 7.
  4. Is the point (4, 9) on the line? 2 × 4 + 1 = 9. Yes! ✓
  5. Check: read the question again. Does your answer give what was asked, with the right unit? Work backwards to see that it fits. ✓
Example: how to solve it
1.

The line passes through (0, −7) and (3, −10). Slope k =

2.

Calculate: y = 4x − 6. Find y when x = −4.

3.

Find the equation y = kx + m of the line through (−1, −9) and (2, −3).

4.

The line passes through (0, 3) and (2, 5). Slope k =

5.

The line passes through (−2, −16) and (−1, −12). Slope k =

6.

Calculate: y = 2x. Find y when x = 3.

7.

Calculate: y = x − 2. Find y when x = 4.

8.

Calculate: y = 5x + 7. Find y when x = −2.

9.

The line passes through (0, 4) and (3, −5). Slope k =

10.

The line passes through (1, −4) and (5, −20). Slope k =

11.

Calculate: y = −2x + 4. Find y when x = 1.

12.

The line passes through (−1, 3) and (2, 18). Slope k =

13.

Find the equation y = kx + m of the line through (3, 5) and (6, 2).

14.

Find the equation y = kx + m of the line through (2, 3) and (5, 15).

15.

Calculate: y = −x − 8. Find y when x = −2.

16.

Calculate: y = −2x + 4. Find y when x = −1.

17.

Find the equation y = kx + m of the line through (−4, 1) and (0, −3).

18.

Calculate: y = 5x − 5. Find y when x = 1.

19.

Does the point (2, −6) lie on y = x − 8?

20.

Calculate: y = 5x + 1. Find y when x = −1.

Answer key

  1. 1. −1
  2. 2. y = −22
  3. 3. y = 2x − 7
  4. 4. 1
  5. 5. 4
  6. 6. y = 6
  7. 7. y = 2
  8. 8. y = −3
  9. 9. −3
  10. 10. −4
  11. 11. y = 2
  12. 12. 5
  13. 13. y = −x + 8
  14. 14. y = 4x − 5
  15. 15. y = −6
  16. 16. y = 6
  17. 17. y = −x − 3
  18. 18. y = 0
  19. 19. Yes
  20. 20. y = −4

Created with WorksheetMint

Topics on this worksheet

Areas on this sheet

  • Relationships and change · 20

Step 1 of 5

Choose an area

Your choices

Area
Algebra
Exercise type
Linear functions y = kx + m
Age
14–16 years
Difficulty
Easy
Number of tasks
20
Task format
Calculations
Paper size
US Letter
1. Choose content
Area
More options

How to use the tool

  1. Choose the exercise type linear functions.
  2. Pick age group 12–14 or 14–16, difficulty and calculations, word problems or a mix.
  3. Print or save as PDF. “Create new version” gives new numbers with a matching answer key.

About this generator

Linear functions describe steady change, such as a phone plan or a taxi fare. The sheets start with putting x into y = kx + m, then calculate the slope k from two points, decide whether a point lies on the line and finally find the whole equation from two points. Negative slopes and intercepts appear on the harder levels. The answer key is calculated by the website, so it always matches the tasks. No sign-up is needed and no personal data is collected.

Popular uses

  • Introducing y = kx + m
  • Slope from two points
  • Revision before a test
  • Homework with answer key

More math worksheets by topic

Frequently asked questions

How do I pick the right level?
Choose an age or grade in step 2. Start easier if the pupil is unsure – you can switch anytime and get new problems instantly.
Can I see the problems before printing?
Yes. The sheet shows exactly the problems that will print. Click New problems to swap them.
How do I include an answer key?
Turn on Answer key in the last step. It prints on its own page after the problems, with the same numbering.
What does the question mark next to a problem do?
It opens a step-by-step explanation of the method on screen. It is not printed and does not reveal the answer.
How do I find the slope?
k = (y₂ − y₁) / (x₂ − x₁) using two points on the line.
What does m mean?
m is where the line crosses the y-axis, the value of y when x = 0.

Related Printable Tools