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8th grade · Math · Unit 5 of 15

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.

Texas Essential Knowledge and Skills (TEKS) teks student expectation: 8.4(A); 8.4(B); 8.4(C) · slope as a rate of change, and finding slope and y-intercept

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 Texas

In the Texas Essential Knowledge and Skills (TEKS), this is unit 5 of 15 in 8th grade Math, after Congruent Shapes and before Tables, Graphs & Linear Relations.

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: Texas Education Agency (TEA)

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 = 7x + 29 dollars for x visits. What does 29 mean?

    • The number of visits
    • A one-time fee you pay even with 0 visits
    • The cost of each visit
    • The total for 29 visits

  2. Question 2

    A graph of pay against hours worked is a straight line through (0, 0) and (4, 24). What is the slope, and what does it mean?

    • $24 per hour
    • $4 per hour
    • $6 per hour
    • $7 per hour

  3. Question 3

    What is the slope of the line through (−3, 1) and (−2, −1)?

    • -2
    • -4
    • 1
    • 2

  4. Question 4

    Which equation matches the table?

    xy
    06
    19
    212
    315
    • y = 3x + 6
    • y = 3x + 7
    • y = −3x + 6
    • y = 6x + 3

  5. Question 5

    A graph of pay against hours worked is a straight line through (0, 0) and (4, 48). What is the slope, and what does it mean?

    • $48 per hour
    • $11 per hour
    • $4 per hour
    • $12 per hour

  6. Question 6

    What is the slope of the line through (−1, −3) and (3, 9)?

    • -3
    • 4
    • 3
    • 12

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