A state transportation worker records the number of miles traveled on a thruway and the corresponding tolls. The worker creates a scatter plot of the data and determines that the line of best fit is T (m) = 0.04m + 1.26, where T is the amount of the toll, in dollars, and m is the number of miles traveled on the thruway.

Based on this linear model, how many miles can be traveled on the thruway for each additional $1 increase on the toll?

Question

Mathematics

Immanuel

14 October, 19:27

A state transportation worker records the number of miles traveled on a thruway and the corresponding tolls. The worker creates a scatter plot of the data and determines that the line of best fit is T (m) = 0.04m + 1.26, where T is the amount of the toll, in dollars, and m is the number of miles traveled on the thruway.

Based on this linear model, how many miles can be traveled on the thruway for each additional $1 increase on the toll?

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Asa Walter · Answer 1

Suppose the toll is $10. Then,.04m + 1.26 = 10. We can simplify that to. 04m = 8.74 and again to m = 218.5. Now, suppose the toll is $11. Then,.04m + 1.26 = 11. Going through the same steps as before we find that m = 243.5. So a $10 fair will allow a passenger to travel 218.5 miles while an $11 fare will allow 243.5 miles of travel. The difference between these two is 25 miles. Since the fares are $1 apart, that means each additional $1 increase results in 25 additional miles. More simply, 0.04m gives the slope of the line telling us how many miles are traveled per dollar of fare, which is to say 0.04. So we could divide 1 by. 04 to get the same result.