Julissa is running a 10 -kilometer race at a constant pace. After running for 18 minutes, she completes 2 kilometers. After running for 54 minutes, she completes 6 kilometers. Her trainer writes an equation letting t , the time in minutes, represent the independent variable and k , the number of kilometers, represent the dependent variable. Which equation can be used to represent k , the number of kilometers Julissa runs in t minutes?
Answer
A
k minus 2 is equal to 1 ninth open paren t minus 18 close paren
B
k minus 18 is equal to 9 open paren t minus 2 close paren
C
k minus 2 is equal to 9 open paren t minus 18 close paren
D
k minus 18 is equal to 1 ninth open paren t minus 2 close paren
Explanation
The pace is constant, so the rate is the change in kilometers divided by the change in minutes: (6 − 2) ÷ (54 − 18) = 4 ÷ 36 = 1/9 kilometer per minute. Using the point (t, k) = (18, 2), the point-slope equation is k − 2 = (1/9)(t − 18). This is choice A.
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