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 3x + 57 = y. note that a change can be an increase or a decrease. for an increase, use a positive number. for a decrease, use a negative number. answer the questions below. (a) what was the road’s length when the crew started working?
square miles (b) what is the change per day in the road’s length?
square miles

Explanation:

Step1: Solve part (a)

The equation is \(3x + 57=y\). When the crew started working, \(x = 0\) (number of days worked is 0). Substitute \(x = 0\) into the equation:
\(y=3(0)+57 = 57\)

Step2: Solve part (b)

The equation \(y = 3x+57\) is in slope - intercept form \(y=mx + b\), where \(m\) is the slope (rate of change) and \(b\) is the y - intercept. Here, \(m = 3\), so the change per day in the road's length is 3 miles.

Answer:

(a) 57 miles
(b) 3 miles