The function given is \( y = 3.75 + 1.5(x - 1) \).
To find the rate of change of the cost with respect to the number of miles \( x \), we can identify the coefficient of \( x \) in the equation.
Let's rewrite the equation in a simpler form:
\[ y = 3.75 + 1.5x - 1.5 \]
This simplifies to:
\[ y = 1.5x + 2.25 \]
In this equation, the coefficient of \( x \) (which represents the change in cost per mile) is \( 1.5 \).
Thus, the rate of change of the cost in dollars with respect to the number of miles is:
$1.50 per mile.