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 $3 x+52=y$.
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.
What was the road's length when the crew started working?
miles
What is the change per day in the road's length?
miles
Answer
Final Answer: The road's length when the crew started working was \(\boxed{52}\) miles. The change per day in the road's length is \(\boxed{3}\) miles.
Step 1 ：Let's denote the total length of the road as \(y\) (in miles) and the number of days the crew has worked as \(x\). They are related by the equation \(3x + 52 = y\).
Step 2 ：The length of the road when the crew started working is equivalent to the value of \(y\) when \(x = 0\). Substituting \(x = 0\) into the equation \(3x + 52 = y\), we get \(y = 52\). So, the road's length when the crew started working was \(52\) miles.
Step 3 ：The change in the road's length per day is equivalent to the coefficient of \(x\) in the equation \(3x + 52 = y\), which represents the rate of change of \(y\) with respect to \(x\). So, the change per day in the road's length is \(3\) miles.
Step 4 ：Final Answer: The road's length when the crew started working was \(\boxed{52}\) miles. The change per day in the road's length is \(\boxed{3}\) miles.
