DIRECTIONS: Proportional means y ÷ x is the same in every row (that number is k) and the line goes through (0, 0).
Part A — Fill in the y ÷ x row, then decide.
1.
Hours worked and the pay for them.
Hours
2
3
5
8
Pay ($)
26
39
65
104
y ÷ x
Proportional? k =
2.
A taxi charges a flat $24 when you get in, then $3 for every mile.
Miles
1
2
4
8
Fare ($)
27
30
36
48
y ÷ x
Proportional? k =
3.
Pounds of apples and what they cost.
Pounds
1
3
4
6
Cost ($)
3
9
12
18
y ÷ x
Proportional? k =
4.
A plant was already 8 inches tall when it was measured, and grows 4 inches a week after that.
Weeks
1
2
4
8
Height (in)
12
16
24
40
y ÷ x
Proportional? k =
Part B — Same question, written as equations.
5.
y = 8x Proportional? k =
6.
y = 5x + 7 Proportional? k =
7.
y = x ÷ 4 Proportional? k =
8.
y = 3x − 8 Proportional? k =
Proportional, or Just Rising? — continued
Grade 7 · Proportion · Page 2 of 2
Graph A
Graph B
Part C — Follow each line back toward (0, 0).
9.
Graph A. Reaches (0, 0)? Proportional? y ÷ x =
10.
Graph B. Reaches (0, 0)? Proportional? y ÷ x =
Part D — Explain it.
A phone plan costs $30 a month plus $3 for every gigabyte of data. Riley graphs it, gets a dead straight line, and says “straight line, so it is proportional.” Riley’s graph is drawn correctly. Which test does the plan fail, and how would the graph show it?
“Every time x goes up, y goes up too, so it is proportional.” Is that enough? Name something on this sheet that rises steadily and is not proportional, and say what is missing.