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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, $x$ . $\newline$ What is true about the function? $\newline$ Choices: $\newline$ (A)It is nonlinear because the rate of change is always zero. $\newline$ (B)It is nonlinear because it increases at a constant rate. $\newline$ (C)It is linear because the rate of change is always zero. $\newline$ (D)It is linear because it increases at a constant rate.

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Identify independent and dependent variables

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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

.

\newline

What is true about the function?

\newline

Choices:

\newline

(A)It is nonlinear because the rate of change is always zero.

\newline

(B)It is nonlinear because it increases at a constant rate.

\newline

(C)It is linear because the rate of change is always zero.

\newline

(D)It is linear because it increases at a constant rate.

Analyze Function: Step $1$ : Analyze the function $y = 40x$ to determine its characteristics. $\newline$ 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. $\newline$ 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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