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.

California 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.

Slope = change in y ÷ change in x.
In y = mx + b, m is the slope and b is the starting value.
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

Sample questions

A taste of this unit. In the app, questions change every time and get easier or harder to match your child.

Question 1
What is the slope of the line through (−1, −1) and (3, 7)?
- -2
- 2
- 4
- 8
Question 2
A graph of pay against hours worked is a straight line through (0, 0) and (3, 18). What is the slope, and what does it mean?
- $6 per hour
- $18 per hour
- $7 per hour
- $3 per hour
Question 3
Which equation matches the table?
x y
0 6
1 8
2 10
3 12
- y = 2x + 7
- y = −2x + 6
- y = 2x + 6
- y = 6x + 2
Question 4
A gym charges y = 4x + 36 dollars for x visits. What does 36 mean?
- The cost of each visit
- A one-time fee you pay even with 0 visits
- The number of visits
- The total for 36 visits
Question 5
A gym charges y = 3x + 12 dollars for x visits. What does 12 mean?
- The total for 12 visits
- The cost of each visit
- The number of visits
- A one-time fee you pay even with 0 visits
Question 6
Which equation matches the table?
x y
0 0
1 5
2 10
3 15
- y = 5x + 1
- y = x + 5
- y = 5x
- y = −5x