A construction crew is lengthening a road. Let y represent the total length of the road (in miles). Let represent the number of days the crew has worked. Suppose that x and y are related by the equation 3x+58=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?
What is the change per day in the road's length?
To find the road's length when the crew started working, we need to solve the equation for y when x is equal to zero.
When x = 0, the equation becomes 3(0) + 58 = y.
This simplifies to 0 + 58 = y.
Therefore, when the crew started working, the road's length was 58 miles.
To find the change per day in the road's length, we need to find the ratio of the change in the road's length (y) to the number of days worked (x).
From the given equation, we have 3x + 58 = y.
Since y represents the total length of the road and x represents the number of days worked, the change in the road's length per day can be found by taking the derivative of the equation with respect to x.
The derivative of y with respect to x is 3.
Therefore, the change per day in the road's length is 3 miles.