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 2x + 53 = y. answer the questions below. 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. (a) what was the road’s length when the crew started working? miles (b) what is the change per day in the road’s length? miles

Explanation:

Step1: Analyze part (a)

The equation is \( y = 2x + 53 \). When the crew started working, \( x = 0 \) (number of days is 0). Substitute \( x = 0 \) into the equation: \( y = 2(0)+53 = 53 \). So the road's length when starting is 53 miles.

Step2: Analyze part (b)

The linear equation is in the form \( y = mx + b \), where \( m \) is the slope (rate of change). Here, the equation is \( y = 2x + 53 \), so the slope \( m = 2 \). This means the change per day in the road's length is 2 miles (positive since it's an increase).

Answer:

(a) 53 miles
(b) 2 miles