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8th grade · Math · Unit 11 of 11

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.

Minnesota K-12 Academic Standards benchmark: 8.2.4.1; 8.3.7.1 · slope, the equation y = mx + b, and comparing proportional and non-proportional relationships

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 Minnesota

In the Minnesota K-12 Academic Standards, this is unit 11 of 11 in 8th grade Math, after Functions.

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: Minnesota Department of Education (MDE)

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 (5, 1) and (10, 6)?

    • -1
    • 1
    • 3
    • 5

  2. Question 2

    A graph of pay against hours worked is a straight line through (0, 0) and (3, 15). What is the slope, and what does it mean?

    • $15 per hour
    • $3 per hour
    • $5 per hour
    • $2 per hour

  3. Question 3

    Which equation matches the table?

    xy
    0-3
    12
    27
    312
    • y = 5x − 3
    • y = −5x − 3
    • y = −3x + 5
    • y = 5x − 2

  4. Question 4

    A gym charges y = 7x + 14 dollars for x visits. What does 14 mean?

    • A one-time fee you pay even with 0 visits
    • The number of visits
    • The total for 14 visits
    • The cost of each visit

  5. Question 5

    A graph of pay against hours worked is a straight line through (0, 0) and (5, 65). What is the slope, and what does it mean?

    • $14 per hour
    • $5 per hour
    • $13 per hour
    • $65 per hour

  6. Question 6

    What is the slope of the line through (5, 3) and (7, 7)?

    • -2
    • -1
    • 4
    • 2

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