Cogito
Grade 7 Math · Chapter 2 · Lesson 3
The Graph of a Proportional Relationship
A straight line through the origin.
10 problems · about 18 minutes · 7.RP.A.2
What this lesson teaches
The child recognises a proportional relationship from its graph and reads the constant at x = 1.
- A proportional relationship is a straight line through the origin.
- The height of the line at x = 1 is the constant k.
- Straight alone is not enough — it must also pass through (0, 0).
Warm-Up Review
From earlier lessons. Loosen up before the new work.
3 problemsReview — Telling Proportional from Not: y = 3x + 7. What is y when x = 6?
Answer 25
Why 25.
Review — The Constant of Proportionality: 5 pairs with 35. What is k?
Answer 7
Why 7.
Review — Redrawing at a New Scale: 9 cm at 1 cm to 2 m, redrawn at 1 cm to 3 m. New length in cm?
Answer 6
Why 6 cm.
Warm Up
Straightforward practice. Get the method working first.
3 problemsProportional graph through (4, 24). What is k?
Answer 6
Why k = 6.
Proportional graph through (2, 10). What is k?
Answer 5
Why 10 ÷ 2.
Proportional graph through (5, 15). What is k?
Answer 3
Why 15 ÷ 5.
Build It Up
The same ideas with more to keep track of.
2 problemsMust a proportional graph pass through the origin? Answer 1 for yes, 0 for no.
Answer 1
Why Nothing gives nothing.
If k = 6, what is y when x is 4?
Answer 24
Why y = 6x.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Line: A proportional graph passes through (3, 12). What is k?
Answer 4
Why k = 4.
The Taxi: A taxi charges £3 to start plus £2 a mile. Is it proportional? Answer 1 for yes, 0 for no.
Answer 0
Why No — the line misses the origin.