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8th grade · Math · Unit 17 of 19

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.

New York State Learning Standards learning standard: NY-8.EE.5; NY-8.EE.6; NY-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 New York

In the New York State Learning Standards, this is unit 17 of 19 in 8th grade Math, after Cones, Cylinders & Spheres and before Distance on a Grid.

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: New York State Education Department (NYSED)

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 (5, 85). What is the slope, and what does it mean?

    • $85 per hour
    • $17 per hour
    • $14 per hour
    • $5 per hour

  2. Question 2

    Which equation matches the table?

    xy
    01
    12
    23
    34
    • y = −x + 1
    • y = x + 1
    • y = x + 2

  3. Question 3

    A gym charges y = 7x + 23 dollars for x visits. What does 23 mean?

    • The total for 23 visits
    • The cost of each visit
    • The number of visits
    • A one-time fee you pay even with 0 visits

  4. Question 4

    What is the slope of the line through (2, 2) and (4, −4)?

    • -3
    • -6
    • 3
    • 2

  5. Question 5

    A gym charges y = 6x + 33 dollars for x visits. What does 33 mean?

    • A one-time fee you pay even with 0 visits
    • The total for 33 visits
    • The number of visits
    • The cost of each visit

  6. Question 6

    A graph of pay against hours worked is a straight line through (0, 0) and (5, 30). What is the slope, and what does it mean?

    • $5 per hour
    • $6 per hour
    • $30 per hour
    • $9 per hour

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