Interpret slope of line in context of problem

Question

The average cost of tuition at a community college was $3,520 in 2005 and the cost has increased somewhat linearly to $4,414 in 2017 let x be the number of years since 2000 and let y be the cost of tuition.

Interpret the slope of the line in the context of the problem using a complete sentence.

Answer 1

Assuming that the rate of increase is linear from 2000 (a fair assumption given the phrasing of the question but not at all a fair assumption for most cases), we have two data points:

(x = 2005 - 2000 = 5 , y = 3520) and (x = 2017 - 2000 = 17 , y = 4414). (5 , 3520) and (17 , 4414)

y = mx + b, where we only need one formula given two data points, which is m = (y2-y1)/(x2-y1)

m = (4414 - 3520)/(17-5) = 74.5.

I agree with another user that the question is poorly presented, but I think this is an appropriate answer given its apparent level. b should be appropriately calculated first

Answer 2

The rate at which the cost of tuition at a community college increased is $74.50 per year since 2000.