Proportional — Grade 7 Accelerated, what it means and where it is taught
Two quantities with a constant ratio: yx = k always.
Taught in Grade 7 Accelerated.
Where it is taught
What it rests on
Work through these first if this one does not settle.
- Ratio — A comparison of two quantities, like 3 cups flour to 2 cups water.
What uses it later
This idea is needed for:
- Origin — The point (0, 0), which every proportional graph passes through.
- Similar figures — Same shape, different size: equal angles, proportional sides.
- Constant speed — A rate that does not change, so distance and time stay proportional.
Practise this idea
11 questions in the course bank use Proportional, in Proportional Relationships, Representing Other Algebraic Relationships, Slope & Unit Rate. The first 8 are below; the rest are in those units.
Problem 1
Which equation represents a proportional relationship?
- y = 4x
- y = 4x + 3
- y = 4x
- y = x2
Worked answer
y = 4x
y = 4x has the form y = kx with k = 4.
The others add a constant, divide, or square — none is proportional.
Problem 2
A proportional relationship passes through (3, 21). Find k.
Worked answer
7
k = 213 = 7
So y = 7x.
Problem 3
Every proportional graph must pass through which point?
- (1, 1)
- (0, 0)
- (1, 0)
- (0, 1)
Worked answer
(0, 0)
Zero of one means zero of the other, so the line goes through the origin (0, 0).
Problem 4
Which relationship is NOT proportional?
- 8 apples for $4; 12 apples for $6
- A car travelling 50 miles every hour
- A gym charging $25 to join plus $15 a month
- 3 cups of flour per dozen cookies
Worked answer
A gym charging $25 to join plus $15 a month
With the gym, zero months still costs $25, so the graph misses (0,0).
It is linear (y = 15x + 25) but not proportional.
Problem 5
A proportional graph passes through (4, 10). Find k as a decimal.
Worked answer
2.5
k = 104 = 2.5
Problem 6
In a proportional relationship, y = 45 when x = 12. Find x when y = 75.
Worked answer
20
k = 4512 = 3.75
75 = 3.75x
x = 75 ÷ 3.75 = 20
Problem 7
Line A passes through (2, 5) and line B through (3, 7). Both are proportional. Which is steeper?
- Line A
- Line B
- They have the same steepness
Worked answer
Line A
A: k = 52 = 2.5
B: k = 73 ≈ 2.33
2.5 > 2.33, so A is steeper.
Problem 8
A table shows x = 2, 4, 7 with y = 7, 14, 24. Is it proportional?
- Yes, with k = 3.5
- No — the last pair breaks the pattern
- No — it does not pass through the origin
Worked answer
No — the last pair breaks the pattern
72 = 3.5 and 144 = 3.5 — so far so good
But 247 ≈ 3.43, which does not match
One disagreeing row is enough to rule it out.