Question

The function y = 125 + 75x can be used to determine the cost in dollars for a painting job of x hours. What is the rate of change of the cost in dollars with respect to the number of hours spent painting? *

Answer 1

These are examples of a dependent variable and an independent variable. Because y is the variable which is changing, it is considered the dependent variable (as its value DEPENDS on the independent variable). By process of elimination, x is the independent variable (make sure you see why before reading on).

With the knowledge that x is the independent variable in mind, look at the coefficient of x in the equation (y = 125 + 75x). If the coefficient of the linear term (with x) is 75, then the rate of change you're looking for is... 75.

Please try to learn from this solution.