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.
Alabama Course of Study content standard: 8.7; 8.8; 8.9 · proportional relationships, slope as the unit rate, and 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
Slope & Rate of Change in Alabama
In the Alabama Course of Study, 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.
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
Which equation matches the table?
x y 0 3 1 9 2 15 3 21 - y = 6x + 4
- y = −6x + 3
- y = 3x + 6
- y = 6x + 3
y = 6x + 3
Hint: The y-value at x = 0 is b. The change in y for each 1 in x is the slope m.
Question 2
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?
- $6 per hour
- $16 per hour
- $108 per hour
- $18 per hour
$18 per hour
Hint: Slope = 108 ÷ 6 = 18: the pay for each hour.
Question 3
What is the slope of the line through (5, 3) and (8, −6)?
- 3
- -4
- -9
- -3
-3
Hint: Slope = change in y ÷ change in x = (−6 − 3) ÷ (8 − 5).
Question 4
A gym charges y = 6x + 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 cost of each visit
- The number of visits
A one-time fee you pay even with 0 visits
Hint: The y-intercept (b) is the value when x = 0: the starting amount.
Question 5
Which equation matches the table?
x y 0 7 1 3 2 -1 3 -5 - y = −4x + 8
- y = −4x + 7
- y = 4x + 7
- y = 7x − 4
y = −4x + 7
Hint: The y-value at x = 0 is b. The change in y for each 1 in x is the slope m.
Question 6
A graph of pay against hours worked is a straight line through (0, 0) and (5, 80). What is the slope, and what does it mean?
- $15 per hour
- $80 per hour
- $16 per hour
- $5 per hour
$16 per hour
Hint: Slope = 80 ÷ 5 = 16: the pay for each hour.