Question

Caleb made the table below to show the number of hours he works and the amounts he earns over a four-week period.


Caleb’s Earnings
Hours
12
15
18
21
Earnings
(in dollars)
140
170
200
230

Which describes whether the relationship between the earnings and the number of hours represents a direct variation?
He earns 20 more than 10 times the number of hours he works each week, so the earnings vary directly with the hours.
The earnings increase by 30 for every increase of 3 hours, so the earnings vary directly with the hours.
The ratios of earnings to hours are not the same each week, so the earnings do not vary directly with the hours.
The earnings increase at a steady rate, so the earnings do not vary directly with the hours.

Answer 1

Answer: The ratios are not the same each week, so the earnings do not vary directly with the hours.

Work: 140/12 ≈ 11.67, 170/15 ≈ 11.33, 200/18 ≈ 11.11, 230/21 ≈ 10.95 — these are not constant. The data fit y = 10x + 20 (earnings = 10·hours + 20), not y = kx, so it is not a direct variation.