Cogito
Grade 8 Math · Chapter 6 · Lesson 3
Rate of Change and Starting Value
Building a function from a situation.
10 problems · about 19 minutes · 8.F.B.4
What this lesson teaches
The child constructs a linear function from a description, a table, or two points.
- A linear function is fixed by its rate of change and its starting value.
- The rate comes from any two points; the start is y when x is nought.
- Together they give y = mx + b.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
3 problemsReview — Linear and Nonlinear Functions: 4, 10, 16, 22. Constant rise?
Answer 6
Why 6, so it is linear.
Review — What a Function Is: Rule "multiply by 4 then add 1". What comes out when 5 goes in?
Answer 21
Why 21.
Review — Solving a System by Elimination: x + y = 12 and x − y = 4. What is x?
Answer 8
Why x = 8.
Warm Up
Straightforward practice. Get the method working first.
3 problemsThrough (0, 7) and (3, 19). What is the rate?
Answer 4
Why 4.
Starts at 6, rises 2 each step. What is y at x = 4?
Answer 14
Why 6 + 8.
y = 5x + 3. What is the starting value?
Answer 3
Why y when x is nought.
Build It Up
The same ideas with more to keep track of.
2 problemsThrough (0, 4) and (2, 10). What is the rate?
Answer 3
Why 6 ÷ 2.
y = −2x + 20. What is y at x = 5?
Answer 10
Why −10 + 20.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Tank: y = −4x + 50. How many litres after 10 minutes?
Answer 10
Why 10 litres.
The Empty Tank: y = −4x + 50. After how many minutes is it empty?
Answer 12.5
Why 12.5 minutes.