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Compare functions: 8th grade math

Compare functions in different representations. A free 8th grade lesson plan, a question set with answers and a printable sheet with its key. Copy it and make it yours.

Lesson plan

Goal

  • Students can do this: compare functions in different representations.

Teach (10 min)

  • 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.
  • Work one example on the board while students say each step aloud, then do one together.

Practise (15 min)

  • Students work the printable sheet in pairs, then alone.
  • Or practise it as a game with no sign-up: https://peabody.kids/math/lines.compareLin?lesson=8-lines-compare-1&at=8

Exit ticket (5 min)

  • Three questions on a slip:
  • 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)?
  • 2. Line A is y = 4x + 3. Line B passes through (1, 4) and (2, 6). Which line has the greater y-intercept (the greater y when x = 0)?
  • 3. Line A is y = x + 7. Line B passes through (1, 4) and (3, 8). Which line has the greater rate of change (slope)?

Question set

10 questions that read in words, easiest first. Questions that need a picture are on the printable sheet below.

  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)?
  2. Line A is y = 4x + 3. Line B passes through (1, 4) and (2, 6). Which line has the greater y-intercept (the greater y when x = 0)?
  3. Line A is y = x + 7. Line B passes through (1, 4) and (3, 8). Which line has the greater rate of change (slope)?
  4. Line A is y = x + 8. Line B passes through (3, 24) and (4, 30). Which line has the greater rate of change (slope)?
  5. Line A is y = 3x + 9. Line B passes through (3, 14) and (5, 20). Which line has the greater y-intercept (the greater y when x = 0)?
  6. Line A is y = 6x + 8. Line B passes through (1, 12) and (4, 21). Which line has the greater rate of change (slope)?
  7. Line A is y = 4x + 8. Line B has the table: x = 0, y = 2; x = 1, y = 3; x = 2, y = 4. Which line has the greater rate of change (slope)?
  8. Line A is y = 5x + 9. Line B starts at y = 2 when x = 0 and changes by 3 for each 1 that x goes up. Which line has the greater rate of change (slope)?
  9. Line A is y = −5x + 6. Line B has the table: x = 0, y = 4; x = 1, y = 5; x = 2, y = 6. Which line has the greater y-intercept (the greater y when x = 0)?
  10. Line A is y = −2x − 6. Line B starts at y = 6 when x = 0 and changes by −3 for each 1 that x goes up. Which line has the greater rate of change (slope)?
Answers
  1. Line B
  2. Line A
  3. Line B
  4. Line B
  5. Line A
  6. Line A
  7. Line A
  8. Line A
  9. Line A
  10. Line A

Printable sheet

Name: ____________________   Date: ____________

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?
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

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