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8th grade · Math · Unit 16 of 17

Slope & Rate of Change

Rise over run

What your child practices

Finding slope from two points or a table, reading slope as a unit rate, writing y = mx + b, and saying what the intercept means.

Maine Learning Results learning standard: 8.EE.B.5; 8.EE.B.6; 8.F.B.4 · slope as the unit rate and writing lines as y = mx + b

How we explain it

Children can open this short lesson before they practice.

  1. Slope = change in y ÷ change in x.
  2. In y = mx + b, m is the slope and b is the starting value.
  3. For a proportional graph, the slope is the unit rate.

Example: What is the slope through (1, 2) and (4, 11)? Change in y: 11 − 2 = 9. Change in x: 4 − 1 = 3. 9 ÷ 3 = 3. Answer: 3

Slope & Rate of Change in Maine

In the Maine Learning Results, this is unit 16 of 17 in 8th grade Math, after Cones, Cylinders & Spheres and before Two-Way Tables.

Gradelings describes a child's practice on this unit as Beginning, Approaching, Meeting or Exceeding (Four practice steps). That reflects practice, not a report-card mark: the teacher decides the mark.

Source: Maine Department of Education

Sample questions

A taste of this unit. In the app, questions change every time and get easier or harder to match your child.

  1. Question 1

    A graph of pay against hours worked is a straight line through (0, 0) and (4, 36). What is the slope, and what does it mean?

    • $9 per hour
    • $4 per hour
    • $6 per hour
    • $36 per hour

  2. Question 2

    A gym charges y = 4x + 37 dollars for x visits. What does 37 mean?

    • The cost of each visit
    • The total for 37 visits
    • A one-time fee you pay even with 0 visits
    • The number of visits

  3. Question 3

    What is the slope of the line through (−5, 3) and (0, 8)?

    • 5
    • -1
    • 4
    • 1

  4. Question 4

    Which equation matches the table?

    xy
    0-5
    10
    25
    310
    • y = −5x + 5
    • y = 5x − 5
    • y = 5x − 4
    • y = −5x − 5

  5. Question 5

    A gym charges y = 5x + 38 dollars for x visits. What does 38 mean?

    • The cost of each visit
    • The number of visits
    • A one-time fee you pay even with 0 visits
    • The total for 38 visits

  6. Question 6

    A graph of pay against hours worked is a straight line through (0, 0) and (5, 60). What is the slope, and what does it mean?

    • $5 per hour
    • $12 per hour
    • $14 per hour
    • $60 per hour

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