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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.

Alaska content standards learning standard: 8.EE.5; 8.EE.6; 8.F.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 Alaska

In the Alaska content standards, 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: Alaska Department of Education and Early Development

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

    What is the slope of the line through (0, 1) and (1, −3)?

    • 4
    • -4
    • -7
    • 1

  2. Question 2

    A gym charges y = 5x + 34 dollars for x visits. What does 34 mean?

    • The number of visits
    • The cost of each visit
    • The total for 34 visits
    • A one-time fee you pay even with 0 visits

  3. Question 3

    Which equation matches the table?

    xy
    0-2
    10
    22
    34
    • y = −2x − 2
    • y = 2x − 2
    • y = 2x − 1
    • y = −2x + 2

  4. Question 4

    A graph of pay against hours worked is a straight line through (0, 0) and (5, 90). What is the slope, and what does it mean?

    • $18 per hour
    • $90 per hour
    • $5 per hour
    • $16 per hour

  5. Question 5

    A graph of pay against hours worked is a straight line through (0, 0) and (6, 42). What is the slope, and what does it mean?

    • $7 per hour
    • $4 per hour
    • $42 per hour
    • $6 per hour

  6. Question 6

    What is the slope of the line through (−2, 0) and (−1, −2)?

    • -2
    • 1
    • -1
    • 2

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