AnswersTransition Mathematics for SeniorsLinear Functions — TestQuestion 10
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Linear Functions — Test

Question 10 • Transition Mathematics for Seniors

Caleb made the given table 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?

Answer
A
The earnings increase by 30 for every increase of 3 hours, so the earnings vary directly with the hours.
B
The earnings increase at a steady rate, so the earnings do not vary directly with the hours.
C
The ratios of earnings to hours are not the same each week, so the earnings do not vary directly with the hours.
D
He earns 20 more than 10 times the number of hours he works each week, so the earnings vary directly with the hours.

Explanation

For a direct variation, earnings divided by hours must be the same each week. Here, $140 ÷ 12 = 11.67, while $170 ÷ 15 ≈ 11.33, so the ratios are not equal. Therefore, earnings do not vary directly with hours; choice C is correct.

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