Interpreting the parameters of a linear function that models a real-world situation

Question

A construction crew is lengthening a road. Let y represent the total length of the road (in miles). Let x represent the number of days the crew has worked. Suppose that x and y are related by the equation 53+2x=y.

Answer the questions below.

What is the change per day in the road's length?

What was the road's length when the crew started working?

Answer 1

rate of change per day is the derivative

y=53 +2x

y' = 2

2 miles = the rate of change per day

original road length is 53 miles

y=53 +2x

y=53 +2(0) = 53 +0 = 53