Skip to the main content
PeabodyMake a free story

🧩 8th grade math · Patterns & Algebra

Linear or not?

In y = mx + b, m multiplies x: it is the slope. b is added on its own: it is where the line crosses the y-axis. In y = 3x − 5 the slope is 3 and the y-intercept is −5. Keep the sign with the number.

Worked example

What is the y-intercept of the line y = 3x − 1?
Answer: −1
In y = mx + b, m is the slope (the number multiplying x) and b is the y-intercept (the number added). For y = 3x − 1: m = 3 and b = −1. Answer: −1.

For grown-ups: Linear functions y = mx + b vs. nonlinear. Below: three problems to try with the worked answers, and a free printable sheet. Children can practise the same skill as a game, with no sign-up and no ads.

  • CCSS 8.F.A.3
What this practises, for teachers

Practices linear functions y = mx + b vs. nonlinear (8.F.A.3). A printable sheet with its answer key, worked answers on the page, no accounts.

▶ Practise it

For your class

🖨️ Printable sheet and key

Try three

  1. What is the slope of the line y = x + 6?
    Show the answer and how
    Answer: 1
    In y = mx + b, m is the slope (the number multiplying x) and b is the y-intercept (the number added). For y = x + 6: m = 1 and b = 6. Answer: 1.
  2. What is the y-intercept of the line y = −2x + 2?
    Show the answer and how
    Answer: 2
    In y = mx + b, m is the slope (the number multiplying x) and b is the y-intercept (the number added). For y = −2x + 2: m = −2 and b = 2. Answer: 2.
  3. What is the slope of the line y = 3x + 5?
    Show the answer and how
    Answer: 3
    In y = mx + b, m is the slope (the number multiplying x) and b is the y-intercept (the number added). For y = 3x + 5: m = 3 and b = 5. Answer: 3.

Before and after

Learn first: Compare functions (8th)

Comes next: Rate and starting value (8th)

Name: ____________________Date: ____________Score: ____ / 12

Linear or not? (8th grade)

  1. What is the slope of the line y = 6x + 4?
  2. What is the slope of the line y = x − 8?
  3. What is the slope of the line y = 3x − 6?
  4. What is the y-intercept of the line y = 3x − 2?
  5. What is the y-intercept of the line y = 6x + 8?
  6. The graph shows the line y = mx + b. Where does the line cross the y-axis? Give the y-intercept b.
    −6−6−5−5−4−4−3−3−2−2−1−1112233445566xy
  7. What is the y-intercept of the line y = 6x + 6?
  8. The graph shows the line y = mx + b. Where does the line cross the y-axis? Give the y-intercept b.
    −6−6−5−5−4−4−3−3−2−2−1−1112233445566xy
  9. What is the slope of the line y = 5x − 6?
  10. The graph shows the line y = mx + b. Where does the line cross the y-axis? Give the y-intercept b.
    −6−6−5−5−4−4−3−3−2−2−1−1112233445566xy
  11. What is the slope of the line y = 2x − 3?
  12. The graph shows the line y = mx + b. Where does the line cross the y-axis? Give the y-intercept b.
    −6−6−5−5−4−4−3−3−2−2−1−1112233445566xy

Answer key

  1. 6
  2. 1
  3. 3
  4. −2
  5. 8
  6. −4
  7. 6
  8. 1
  9. 5
  10. 2
  11. 2
  12. 4

More 8th grade skills: all 8th grade math skills, or every grade at math skills.