Cogito
Grade 8 Math · Chapter 3 · Lesson 4
Unit Rate as Slope
The rate is the steepness.
10 problems · about 18 minutes · 8.EE.B.5
What this lesson teaches
The child interprets the unit rate of a proportional relationship as the slope of its graph.
- For a proportional relationship, the unit rate and the slope are the same number.
- A steeper line means a faster rate.
- Converting both to rates lets a table and a graph be compared.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
3 problemsReview — Slope from Two Points: Through (1, 2) and (4, 11). Slope?
Answer 3
Why 3.
Review — y = mx + b: y = 3x − 4. What is y when x = 6?
Answer 14
Why 14.
Review — Why Slope Is the Same Everywhere: Rise 12, run 4. Slope?
Answer 3
Why 3.
Warm Up
Straightforward practice. Get the method working first.
3 problemsA proportional line through (7, 28). What is its slope?
Answer 4
Why 4.
Through (3, 15). Slope?
Answer 5
Why 15 ÷ 3.
6 kg costs £30. Rate in pounds per kg?
Answer 5
Why 30 ÷ 6.
Build It Up
The same ideas with more to keep track of.
2 problemsOf slopes 3 and 7, which line is steeper? Give the number.
Answer 7
Why More rise per run.
A proportional line through (5, 20). What is y when x is 1?
Answer 4
Why That is the unit rate.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Table: 5 hours earns £40. What is the rate, in pounds per hour?
Answer 8
Why £8 an hour.
The Graph: A proportional line passes through (4, 36). What is its slope?
Answer 9
Why 9.