Skip to the content
Peabody TeachFor teachers and grown-ups

Rate and starting value: 8th grade math

Model with linear functions; rate of change; initial value. 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: model with linear functions; rate of change; initial value.

Teach (10 min)

  • 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.
  • 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.writeEq?lesson=8-lines-writeeq-1&at=8

Exit ticket (5 min)

  • Three questions on a slip:
  • 1. A line passes through (0, 2) and (1, 0). Which equation fits?
  • 2. A line passes through (0, 3) and (1, 0). Which equation fits?
  • 3. A line passes through (0, 4) and (1, 1). Which equation fits?

Question set

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

  1. A line passes through (0, 2) and (1, 0). Which equation fits?
  2. A line passes through (0, 3) and (1, 0). Which equation fits?
  3. A line passes through (0, 4) and (1, 1). Which equation fits?
  4. A line passes through (0, 5) and (1, 1). Which equation fits?
  5. A line passes through (0, 2) and (2, 1). Which equation fits?
  6. A line passes through (0, 3) and (1, 4). Which equation fits?
  7. A line passes through (−2, 1) and (0, −3). Which equation fits?
  8. A savings jar starts with −2 dollars and changes by 4 dollars each week. Let x be the number of weeks and y the dollars in the jar. Which equation fits?
  9. A savings jar starts with 1 dollars and changes by 1/2 dollars each week. Let x be the number of weeks and y the dollars in the jar. Which equation fits?
  10. A savings jar starts with −3 dollars and changes by −3 dollars each week. Let x be the number of weeks and y the dollars in the jar. Which equation fits?
Answers
  1. y = −2x + 2
  2. y = −3x + 3
  3. y = −3x + 4
  4. y = −4x + 5
  5. y = −(1/2)x + 2
  6. y = x + 3
  7. y = −2x − 3
  8. y = 4x − 2
  9. y = (1/2)x + 1
  10. y = −3x − 3

Printable sheet

Name: ____________________   Date: ____________

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?
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

Written by Peabody from its own skill pages. Free, no ads, no sign-in. Children can practise this on Peabody. More from teachers: teacher-shared resources.