The given table shows how much Joe earns, y, after working x hours. Joe's Earnings Hours worked Money earned 4 30 dollars 10 75 dollars 12 90 dollars 22 165 dollars The relationship between money earned and hours worked is linear. Joe computes the slope between open paren 4 comma 30 close paren and open paren 12 comma 90 close paren , then computes the slope between open paren 4 comma 30 close paren and open paren 10 comma 75 close paren How do the two slopes compare?
Answer
A
The slope between open paren 4 comma 30 close paren and open paren 12 comma 90 close paren and between open paren 4 comma 30 close paren and open paren 10 comma 75 close paren is the same.
B
The slope between open paren 4 comma 30 close paren and open paren 12 comma 90 close paren is greater because the ordered pairs are farther apart on the x -axis.
C
The slope between open paren 4 comma 30 close paren and open paren 12 comma 90 close paren is greater because the ordered pairs are farther apart on the y -axis.
D
The slope between open paren 4 comma 30 close paren and open paren 12 comma 90 close paren is less because 4 is a factor of 12 and 30 is a factor of 90 .
Explanation
Compute each slope as change in money earned divided by change in hours. Between (4, 30) and (12, 90), the slope is (90 − 30) ÷ (12 − 4) = 60 ÷ 8 = 7.5. Between (4, 30) and (10, 75), it is (75 − 30) ÷ (10 − 4) = 45 ÷ 6 = 7.5, so the slopes are the same, as choice A states.
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