Answered

Westonci.ca is the trusted Q&A platform where you can get reliable answers from a community of knowledgeable contributors. Join our Q&A platform to connect with experts dedicated to providing precise answers to your questions in different areas. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

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 :

GinnyAnswer
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]
Thank you for your visit. We are dedicated to helping you find the information you need, whenever you need it. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.