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Clayton got a box of chocolates for Valentine's Day. The function $y = 12$ represents the number of chocolates that remain, $y$ , as a function of the number of days that have passed, $x$ . $\newline$ What is true about the function? $\newline$ Choices: $\newline$ (A)It is linear because the rate of change is always $12$ . $\newline$ (B)It is linear because the rate of change is always $0$ . $\newline$ (C)It is nonlinear because the rate of change is undefined. $\newline$ (D)It is nonlinear because $12$ does not represent a rate of change.

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One-step inequalities: word problems

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Q. Clayton got a box of chocolates for Valentine's Day. The function

y = 12

represents the number of chocolates that remain,

y

, as a function of the number of days that have passed,

x

.

\newline

What is true about the function?

\newline

Choices:

\newline

(A)It is linear because the rate of change is always

12

.

\newline

(B)It is linear because the rate of change is always

0

.

\newline

(C)It is nonlinear because the rate of change is undefined.

\newline

(D)It is nonlinear because

12

does not represent a rate of change.

Analyze the function: Analyze the function $y = 12$ . $\newline$ This function means that no matter what value $x$ takes, $y$ always equals $12$ . This indicates a constant function where $y$ does not change as $x$ changes.
Determine the rate of change: Determine the rate of change. $\newline$ In a constant function like $y = 12$ , the change in $y$ over the change in $x$ ( $\Delta y/\Delta x$ ) is $0$ , because $y$ does not change regardless of changes in $x$ .
Identify if linear: Identify if the function is linear. A linear function has the form $y = mx + b$ . Here, $m$ (slope) would be $0$ since the rate of change is $0$ , and $b$ (y-intercept) is $12$ . Thus, the function is linear with a slope of $0$ .

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