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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.

Arizona Academic Standards 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 Arizona

In the Arizona Academic 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: Arizona 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 gym charges y = 2x + 18 dollars for x visits. What does 18 mean?

    • The total for 18 visits
    • A one-time fee you pay even with 0 visits
    • The number of visits
    • The cost of each visit

  2. Question 2

    What is the slope of the line through (−1, 5) and (3, 17)?

    • 12
    • -3
    • 4
    • 3

  3. Question 3

    A graph of pay against hours worked is a straight line through (0, 0) and (4, 32). What is the slope, and what does it mean?

    • $8 per hour
    • $5 per hour
    • $4 per hour
    • $32 per hour

  4. Question 4

    Which equation matches the table?

    xy
    0-5
    1-3
    2-1
    31
    • y = 2x − 4
    • y = 2x − 5
    • y = −2x − 5
    • y = −5x + 2

  5. Question 5

    A graph of pay against hours worked is a straight line through (0, 0) and (6, 108). What is the slope, and what does it mean?

    • $20 per hour
    • $108 per hour
    • $18 per hour
    • $6 per hour

  6. Question 6

    A gym charges y = 6x + 35 dollars for x visits. What does 35 mean?

    • The cost of each visit
    • The total for 35 visits
    • A one-time fee you pay even with 0 visits
    • The number of visits

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