Mark is earning money by mowing lawns over the summer. The function y=40x represents the total number of dollars Mark earns, y, depending on the number of lawns he mows, x.What is true about the function?Choices:(A)It is nonlinear because the rate of change is always zero.(B)It is nonlinear because it increases at a constant rate.(C)It is linear because the rate of change is always zero.(D)It is linear because it increases at a constant rate.
Q. Mark is earning money by mowing lawns over the summer. The function y=40x represents the total number of dollars Mark earns, y, depending on the number of lawns he mows, x.What is true about the function?Choices:(A)It is nonlinear because the rate of change is always zero.(B)It is nonlinear because it increases at a constant rate.(C)It is linear because the rate of change is always zero.(D)It is linear because it increases at a constant rate.
Analyze Function: Step 1: Analyze the function y=40x to determine its characteristics.The function y=40x shows that for each lawn mowed, Mark earns $40. This is a direct multiplication relationship between the number of lawns mowed (x) and the total earnings (y).
Identify Type: Step 2: Identify the type of function.Since the earnings increase by a constant amount ($\(40\)) for each additional lawn mowed, the function has a constant rate of change. This constant rate of change indicates a linear function.
Match Characteristics: Step \(3\): Match the function's characteristics with the given choices.\(\newline\)The function is not nonlinear; it is linear because it increases by a constant rate (not zero) as more lawns are mowed. Therefore, the correct choice is:\(\newline\)(D) It is linear because it increases at a constant rate.
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