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🧩 8th grade math · Patterns & Algebra

Rate and starting value

Find the slope from two points. Find b: the y-value where x = 0. Then write y = mx + b. Check by trying a point in your equation. If it does not fit, the equation is wrong.

Worked example

A line passes through (0, −2) and (1, −1). Which equation fits?
Answer: y = x − 2
Find the slope from two points: change in y over change in x = 1. Then find b, where the line crosses x = 0: it is −2. So y = x − 2. Answer: y = x − 2.

For grown-ups: Model with linear functions; rate of change; initial value. 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.B.4
What this practises, for teachers

Practices model with linear functions; rate of change; initial value (8.F.B.4). A printable sheet with its answer key, worked answers on the page, no accounts.

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For your class

🖨️ Printable sheet and key

Try three

  1. The graph shows a line through the dots. Which equation fits?
    −6−6−5−5−4−4−3−3−2−2−1−1112233445566xy
    Show the answer and how
    Answer: y = −2x + 3
    Find the slope from two points: change in y over change in x = −2. Then find b, where the line crosses x = 0: it is 3. So y = −2x + 3. Answer: y = −2x + 3.
  2. The graph shows a line through the dots. Which equation fits?
    −6−6−5−5−4−4−3−3−2−2−1−1112233445566xy
    Show the answer and how
    Answer: y = 2x + 3
    Find the slope from two points: change in y over change in x = 2. Then find b, where the line crosses x = 0: it is 3. So y = 2x + 3. Answer: y = 2x + 3.
  3. A line passes through (0, −1) and (2, 5). Which equation fits?
    Show the answer and how
    Answer: y = 3x − 1
    Find the slope from two points: change in y over change in x = 3. Then find b, where the line crosses x = 0: it is −1. So y = 3x − 1. Answer: y = 3x − 1.

Before and after

Learn first: Linear or not? (8th)

Comes next: Graphs that tell stories (8th)

Name: ____________________Date: ____________Score: ____ / 12

Rate and starting value (8th grade)

  1. A line passes through (0, −5) and (1, −1). Which equation fits?
  2. The graph shows a line through the dots. Which equation fits?
    −6−6−5−5−4−4−3−3−2−2−1−1112233445566xy
  3. A line passes through (0, −5) and (1, 0). Which equation fits?
  4. A line passes through (0, −3) and (1, −2). Which equation fits?
  5. The graph shows a line through the dots. Which equation fits?
    −6−6−5−5−4−4−3−3−2−2−1−1112233445566xy
  6. A line passes through (0, −5) and (2, −4). Which equation fits?
  7. The graph shows a line through the dots. Which equation fits?
    −6−6−5−5−4−4−3−3−2−2−1−1112233445566xy
  8. A savings jar starts with 5 dollars and changes by 1 dollars each week. Let x be the number of weeks and y the dollars in the jar. Which equation fits?
  9. The graph shows a line through the dots. Which equation fits?
    −6−6−5−5−4−4−3−3−2−2−1−1112233445566xy
  10. The graph shows a line through the dots. Which equation fits?
    −6−6−5−5−4−4−3−3−2−2−1−1112233445566xy
  11. The graph shows a line through the dots. Which equation fits?
    −6−6−5−5−4−4−3−3−2−2−1−1112233445566xy
  12. A savings jar starts with 1 dollars and changes by 1 dollars each week. Let x be the number of weeks and y the dollars in the jar. Which equation fits?

Answer key

  1. y = 4x − 5
  2. y = −4x − 2
  3. y = 5x − 5
  4. y = x − 3
  5. y = −x − 3
  6. y = (1/2)x − 5
  7. y = (1/2)x − 3
  8. y = x + 5
  9. y = x − 5
  10. y = −3x + 1
  11. y = x + 3
  12. y = x + 1

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