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🧩 8th grade math · Patterns & Algebra

Compare functions

Find each line's slope and y-intercept in the same way, then compare the numbers. Steeper means a bigger size of slope, ignoring the sign. A slope of −5 is steeper than 3.

Worked example

Line A is y = 6x. Line B passes through (2, 5) and (5, 8). Which line has the greater y-intercept (the greater y when x = 0)?
Answer: Line B
Find the y-intercept of each line. Line A: b = 0. Line B: b = 3. Answer: Line B.

For grown-ups: Compare functions in different representations. 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.2
What this practises, for teachers

Practices compare functions in different representations (8.F.A.2). 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. Line A is y = 2x + 2. Line B passes through (2, 12) and (3, 16). Which line has the greater rate of change (slope)?
    Show the answer and how
    Answer: Line B
    Find the slope of each line. Line A: slope 2. Line B: slope 4. Answer: Line B.
  2. Line A is y = 4x − 3. Line B has the table: x = 0, y = 2; x = 1, y = 0; x = 2, y = −2. Which line is steeper?
    Show the answer and how
    Answer: Line A
    Find the slope of each line. Line A: slope 4. Line B: slope −2. Steepness uses the size of the slope, ignoring the sign: 4 and 2. Answer: Line A.
  3. Line A is y = −3x − 1. Line B passes through (1, −8) and (4, −20). Which line has the greater rate of change (slope)?
    Show the answer and how
    Answer: Line A
    Find the slope of each line. Line A: slope −3. Line B: slope −4. Answer: Line A.

Before and after

Learn first: What is a function? (8th)

Comes next: Linear or not? (8th)

Name: ____________________Date: ____________Score: ____ / 12

Compare functions (8th grade)

  1. Line A is y = 6x + 6. Line B passes through (3, 6) and (4, 7). Which line has the greater rate of change (slope)?
  2. Line A is y = 6x + 5. Line B passes through (2, 11) and (4, 21). Which line has the greater y-intercept (the greater y when x = 0)?
  3. Line A is y = 6x + 9. Line B passes through (1, 9) and (4, 15). Which line has the greater y-intercept (the greater y when x = 0)?
  4. Line A is y = 4x + 1. Line B passes through (2, 9) and (3, 12). Which line has the greater rate of change (slope)?
  5. Line A is y = x + 5. Line B passes through (3, 16) and (5, 22). Which line has the greater y-intercept (the greater y when x = 0)?
  6. Line A is y = 2x + 3. Line B has the table: x = 0, y = −2; x = 1, y = 2; x = 2, y = 6. Which line is steeper?
  7. Line A is y = −3x + 2. Line B passes through (2, −8) and (4, −16). Which line has the greater rate of change (slope)?
  8. Line A is y = 5x + 2. Line B passes through (3, 2) and (5, 0). Which line is steeper?
  9. Line A is y = 3x + 5. Line B starts at y = 4 when x = 0 and changes by −3 for each 1 that x goes up. Which line has the greater y-intercept (the greater y when x = 0)?
  10. Line A is y = 4x. Line B has the table: x = 0, y = 4; x = 1, y = 5; x = 2, y = 6. Which line has the greater rate of change (slope)?
  11. Line A is y = x − 3. Line B starts at y = 7 when x = 0 and changes by 4 for each 1 that x goes up. Which line is steeper?
  12. Line A is y = x − 5. Line B starts at y = −1 when x = 0 and changes by 6 for each 1 that x goes up. Which line is steeper?

Answer key

  1. Line A
  2. Line A
  3. Line A
  4. Line A
  5. Line B
  6. Line B
  7. Line A
  8. Line A
  9. Line A
  10. Line A
  11. Line B
  12. Line B

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