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 + 59 = yAnswer 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.What is the change per day in the road's length?milesWhat was the road's length when the crew started working?miles

Answer 1

`\begin{gathered} (a)\text{ }3\text{ miles} \\ \\ (b)\text{ }59\text{ miles} \end{gathered}`

Step-by-step explanation

We are given an equation that represents the total length of the road:

`3x+59=y`

This equation is a linear equation. The general form of a linear equation is:

`y=mx+b`

where m = slope/rate of change

b = y-intercept

(a) The change per day in the road's length is represented by the slope/rate of change of the equation.

Comparing the given equation with the general equation, we see that the rate of change is 3.

Therefore, the change per day in the road's length is:

`3\text{ miles}`

(b) The road's length when the crew started working represents the initial value of the length of the road. This is represented by the y-intercept of the equation.

Comparing the given equation with the general equation, we see that the y-intercept is 59.

Therefore, the road's length when the crew started working is:

`59\text{ miles}`