Answer :
Final answer:
To express the total time required for a painting job as a linear equation, we consider the setup time of 4 hours as a constant and add one hour for every 1,000 square feet to be painted. The linear equation is T = 4 + x, where T is the total time in hours and x is the number of thousands of square feet to be painted. So, the correct answer is option a.
Explanation:
When considering the time it takes to complete a painting job, we need to create a linear equation. This equation will help us determine the total time required based on the size of the area being painted. Given that the setup time for a painting job is four hours, we can denote this constant time as c, where c = 4 hours.
Additionally, we are told that it takes one hour to paint every 1,000 square feet. If we let x represent the number of thousands of square feet to be painted, then the total time in hours T needed to complete the job can be expressed as T = c + 1*x. Substituting the setup time into the equation gives us T = 4 + x. This is our linear equation representing the total time T, in hours, to complete the painting job.
The variable x is the number of 1,000 square foot units to be painted. Remembering that the setup time doesn't change regardless of the painting area, this equation effectively captures both the fixed setup time and the variable time based on the painting area. To use this equation, simply insert the number of thousands of square feet into the variable x, and calculate T to find the total time required for the painting job.
The correct option to express this information in a linear equation is Option E.
