Final answer:
The rate of change in a painter's earnings is their hourly pay rate. If a painter gets a $2 raise from an original pay of $10 per hour, the rate of change is 20% or 0.20. This same concept applies when calculating total earnings based on a fixed salary and a variable hourly rate.
Step-by-step explanation:
To determine the rate of change of a painter's total earnings, we evaluate how payment changes with respect to the number of hours worked. The rate of change represents the painter's hourly pay rate, which is the slope of the line in a linear equation that relates total earnings to hours worked. For example, if the painter earns a fixed salary plus an additional amount per hour, and if we suppose that the job pays $10 per hour, then a raise would be a change in this hourly rate.
Likewise, if a painter's pay goes from $10 to $12 per hour due to a $2 raise, the rate of change in their earnings is the raise amount divided by the original hourly rate. Applying the given percentage change formula, the rate of increase is $2/$10 which equals 20% or 0.20 when expressed as a decimal. This calculation assists us in understanding how earnings grow with each additional hour worked.
When looking at a linear relationship, like the one involving a fixed amount and a variable hourly rate, you can draw from the example where a job's setup time is four hours plus one hour for every 1000 square feet (as mentioned in the provided reference materials). The setup time would be the initial fixed amount while the one-hour-per-1000 square feet serves as the rate of change in the total time required to complete a job with respect to each 1000 square feet increment.