Proportional Relationships — Mixed

Check yes or no: is the relationship proportional? Divide y by x for every column — equal ratios mean proportional.

ExampleA shop charges a $10 joining fee on top of the price. The table shows dollars earned against hours worked.

hours worked	1	2	4	5
dollars earned	$25.00	$40.00	$70.00	$85.00

Are the two quantities in a proportional relationship?
yesno

Why: The ratios are $25.00 ÷ 1 = $25.00, $40.00 ÷ 2 = $20.00, $70.00 ÷ 4 = $17.50, $85.00 ÷ 5 = $17.00 — they are not all equal. The fixed $10.00 is charged once however much you buy, so doubling the hours does not double the total. Graphed, the line would miss (0, 0).

1.A shop charges a $3 service charge on top of the price. The table shows dollars earned against hours worked.
hours worked 1 2 4 5
dollars earned $21.00 $39.00 $75.00 $93.00
Are the two quantities in a proportional relationship?
yesno
Why?
2.In 8 minutes, Ella records 16 pages. Find the constant of proportionality and say what it means here.
3.The table shows cost in dollars against pounds of apples when apples cost the same for every pound.
pounds of apples 3 4 6 9
cost in dollars $4.50 $6.00 $9.00 $13.50
Write an equation linking x and y, then use it to find y when x = 18.
4.
The graph shows miles traveled against hours traveled when the train travels at a constant speed. What do the points (0, 0) and (1, 4) mean in this situation, and what is the constant of proportionality?
5.A shop charges by weight only. The table shows cost in dollars against pounds of apples.
pounds of apples 1 2 4 5
cost in dollars $2.00 $4.00 $8.00 $10.00
Are the two quantities in a proportional relationship?
yesno
Why?

hours worked	1	2	4	5
dollars earned	$21.00	$39.00	$75.00	$93.00

pounds of apples	3	4	6	9
cost in dollars	$4.50	$6.00	$9.00	$13.50

pounds of apples	1	2	4	5
cost in dollars	$2.00	$4.00	$8.00	$10.00