College algebra

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 X and y are related by the equation 4x+52=y

what is the change per day in the roads length?

what was the roads length when the crew started working ?

Answer 1

When the crew started working, that means that there has been 0 days of work done to the road. So you plug 0 into "x":

4(0)+52=y

y=52 miles

The road was 52 miles long when the crew started working. Now recognize that the function is linear, so the change per day is constant. The change per day is equal to the slope of the function, 4. You can visualize this by plugging in 1 into "x" and getting:

4(1)+52=y y=56, which is 4 more miles than the previous day.