Welcome to Westonci.ca, your go-to destination for finding answers to all your questions. Join our expert community today! Ask your questions and receive accurate answers from professionals with extensive experience in various fields on our platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

Select the table that represents a linear function. (Graph them if necessary.)

A.
\begin{tabular}{|c|c|c|c|c|}
\hline
[tex]$x$[/tex] & 0 & 1 & 2 & 3 \\
\hline
[tex]$y$[/tex] & 10 & 9 & 7 & 4 \\
\hline
\end{tabular}

B.
\begin{tabular}{|c|c|c|c|c|}
\hline
[tex]$x$[/tex] & 0 & 1 & 2 & 3 \\
\hline
[tex]$y$[/tex] & 8 & 6 & 7 & 5 \\
\hline
\end{tabular}

C.
\begin{tabular}{|c|c|c|c|c|}
\hline
[tex]$x$[/tex] & 0 & 1 & 2 & 3 \\
\hline
[tex]$y$[/tex] & 11 & 8 & 5 & 2 \\
\hline
\end{tabular}

D.
\begin{tabular}{|c|c|c|c|c|}
\hline
[tex]$x$[/tex] & 0 & 1 & 2 & 3 \\
\hline
[tex]$y$[/tex] & 0 & 2 & 5 & 8 \\
\hline
\end{tabular}

Sagot :

To determine which table represents a linear function, we'll check the differences between the [tex]\( y \)[/tex]-values for each table. A table represents a linear function if the differences between consecutive [tex]\( y \)[/tex]-values are constant.

Let's examine each table step-by-step:

### Table A:
[tex]\[ \begin{array}{|c|c|c|c|c|} \hline x & 0 & 1 & 2 & 3 \\ \hline y & 10 & 9 & 7 & 4 \\ \hline \end{array} \][/tex]

Differences between [tex]\( y \)[/tex]-values:
[tex]\[ \begin{align*} 9 - 10 &= -1 \\ 7 - 9 &= -2 \\ 4 - 7 &= -3 \\ \end{align*} \][/tex]

The differences are [tex]\(-1\)[/tex], [tex]\(-2\)[/tex], and [tex]\(-3\)[/tex], which are not constant. So, Table A does not represent a linear function.

### Table B:
[tex]\[ \begin{array}{|c|c|c|c|c|} \hline x & 0 & 1 & 2 & 3 \\ \hline y & 8 & 6 & 7 & 5 \\ \hline \end{array} \][/tex]

Differences between [tex]\( y \)[/tex]-values:
[tex]\[ \begin{align*} 6 - 8 &= -2 \\ 7 - 6 &= 1 \\ 5 - 7 &= -2 \\ \end{align*} \][/tex]

The differences are [tex]\(-2\)[/tex], [tex]\(1\)[/tex], and [tex]\(-2\)[/tex], which are not constant. So, Table B does not represent a linear function.

### Table C:
[tex]\[ \begin{array}{|c|c|c|c|c|} \hline x & 0 & 1 & 2 & 3 \\ \hline y & 11 & 8 & 5 & 2 \\ \hline \end{array} \][/tex]

Differences between [tex]\( y \)[/tex]-values:
[tex]\[ \begin{align*} 8 - 11 &= -3 \\ 5 - 8 &= -3 \\ 2 - 5 &= -3 \\ \end{align*} \][/tex]

The differences are [tex]\(-3\)[/tex] each time, which are constant. Thus, Table C represents a linear function.

### Table D:
[tex]\[ \begin{array}{|c|c|c|c|c|} \hline x & 0 & 1 & 2 & 3 \\ \hline y & 0 & 2 & 5 & 8 \\ \hline \end{array} \][/tex]

Differences between [tex]\( y \)[/tex]-values:
[tex]\[ \begin{align*} 2 - 0 &= 2 \\ 5 - 2 &= 3 \\ 8 - 5 &= 3 \\ \end{align*} \][/tex]

The differences are [tex]\(2\)[/tex], [tex]\(3\)[/tex], and [tex]\(3\)[/tex], which are not constant. So, Table D does not represent a linear function.

From our step-by-step checks, we can conclude that the table representing a linear function is:

[tex]\[ \text{Table C} \][/tex]