Proportional Relationships — Drills
Proportional Relationships has 4 drill skills. Each one generates fresh questions every time, with a hint and full worked steps, so you can keep practising a single skill until it settles.
What these drills cover
These questions use 5 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.
- Unit rate — A rate with denominator 1 — how much for exactly one.
- Constant of proportionality — The unit rate, written k, in y = kx.
- Proportional — Two quantities with a constant ratio: yx = k always.
- Origin — The point (0, 0), which every proportional graph passes through.
- Scale — What one grid step is worth — and where the axis starts.
Finding the constant
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A proportional relationship gives y = 24 when x = 4, and y = 54 when x = 9. Find y when x = 19.
Worked answer
114
k = 244 = 6
y = 6x
y = 6 × 19 = 114
Problem 2
A proportional relationship gives y = 32 when x = 4, and y = 56 when x = 7. Find y when x = 23.
Worked answer
184
k = 324 = 8
y = 8x
y = 8 × 23 = 184
Useprop
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
7 tiles cost $84.00. What do 13 tiles cost?
Worked answer
156.00
84.00 ÷ 7 = $12.00 each
12.00 × 13 = $156.00
Problem 2
6 candles cost $12.00. What do 21 candles cost?
Worked answer
42.00
12.00 ÷ 6 = $2.00 each
2.00 × 21 = $42.00
Identifying
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Which equation represents a proportional relationship?
- y = 6x
- y = 6x
- y = 6x + 8
- y = x2 + 6
Worked answer
y = 6x
y = 6x has the form y = kx with k = 6.
The others add a constant, divide, or square — none is proportional.
Comparing
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Line A passes through (6, 12) and line B through (4, 16). Both are proportional. Which is steeper?
- Line B
- They have the same steepness
- Line A
Worked answer
Line B
A: k = 2
B: k = 4
4 > 2, so line B is steeper.
Problem 2
Line A passes through (2, 6) and line B through (4, 14). Both are proportional. Which is steeper?
- Line A
- Line B
- They have the same steepness
Worked answer
Line B
A: k = 3
B: k = 3.5
3.5 > 3, so line B is steeper.