Answered

Welcome to Westonci.ca, where curiosity meets expertise. Ask any question and receive fast, accurate answers from our knowledgeable community. Find reliable answers to your questions from a wide community of knowledgeable experts on our user-friendly Q&A platform. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.

Question 1 of 5

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] & 0 & 0 & -1 & -2 \\
\hline
\end{tabular}

B.
\begin{tabular}{|c|c|c|c|c|}
\hline[tex]$x$[/tex] & 0 & 1 & 2 & 3 \\
\hline[tex]$y$[/tex] & 6 & 12 & 18 & 24 \\
\hline
\end{tabular}

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

D.
\begin{tabular}{|c|c|c|c|c|}
\hline[tex]$x$[/tex] & 0 & 1 & 2 & 3 \\
\hline[tex]$y$[/tex] & 11 & 7 & 5 & 4 \\
\hline
\end{tabular}

Sagot :

GinnyAnswer
To determine which table represents a linear function, we need to check whether the change in [tex]\( y \)[/tex] is proportional to the change in [tex]\( x \)[/tex] for each table.

### Table A
[tex]\[ \begin{tabular}{|c|c|c|c|c|} \hline $x$ & 0 & 1 & 2 & 3 \\ \hline $y$ & 0 & 0 & -1 & -2 \\ \hline \end{tabular} \][/tex]

- Difference in [tex]\( y \)[/tex]: [tex]\(0 - 0 = 0\)[/tex], [tex]\(-1 - 0 = -1\)[/tex], [tex]\(-2 - (-1) = -1\)[/tex]
- Change in [tex]\( x \)[/tex] is consistent (1 unit).

The ratios of change in [tex]\( y \)[/tex] to change in [tex]\( x \)[/tex] are: [tex]\( \frac{0}{1}, \frac{-1}{1}, \frac{-1}{1} \)[/tex]. These ratios are not the same for all intervals.

### Table B
[tex]\[ \begin{tabular}{|l|l|l|l|l|} \hline $x$ & 0 & 1 & 2 & 3 \\ \hline $y$ & 6 & 12 & 18 & 24 \\ \hline \end{tabular} \][/tex]

- Difference in [tex]\( y \)[/tex]: [tex]\(12 - 6 = 6\)[/tex], [tex]\(18 - 12 = 6\)[/tex], [tex]\(24 - 18 = 6\)[/tex]
- Change in [tex]\( x \)[/tex] is consistent (1 unit).

The ratios of change in [tex]\( y \)[/tex] to change in [tex]\( x \)[/tex] are: [tex]\( \frac{6}{1}, \frac{6}{1}, \frac{6}{1} \)[/tex]. These ratios are the same for all intervals, indicating a linear function.

### Table C
[tex]\[ \begin{tabular}{|l|l|l|l|l|} \hline $x$ & 0 & 1 & 2 & 3 \\ \hline $y$ & 3 & 2 & 0 & 1 \\ \hline \end{tabular} \][/tex]

- Difference in [tex]\( y \)[/tex]: [tex]\(2 - 3 = -1\)[/tex], [tex]\(0 - 2 = -2\)[/tex], [tex]\(1 - 0 = 1\)[/tex]
- Change in [tex]\( x \)[/tex] is consistent (1 unit).

The ratios of change in [tex]\( y \)[/tex] to change in [tex]\( x \)[/tex] are: [tex]\( \frac{-1}{1}, \frac{-2}{1}, \frac{1}{1} \)[/tex]. These ratios are not the same for all intervals.

### Table D
[tex]\[ \begin{tabular}{|l|l|l|l|l|} \hline $x$ & 0 & 1 & 2 & 3 \\ \hline $y$ & 11 & 7 & 5 & 4 \\ \hline \end{tabular} \][/tex]

- Difference in [tex]\( y \)[/tex]: [tex]\(7 - 11 = -4\)[/tex], [tex]\(5 - 7 = -2\)[/tex], [tex]\(4 - 5 = -1\)[/tex]
- Change in [tex]\( x \)[/tex] is consistent (1 unit).

The ratios of change in [tex]\( y \)[/tex] to change in [tex]\( x \)[/tex] are: [tex]\( \frac{-4}{1}, \frac{-2}{1}, \frac{-1}{1} \)[/tex]. These ratios are not the same for all intervals.

### Conclusion

Only Table B shows a consistent ratio of the change in [tex]\( y \)[/tex] to change in [tex]\( x \)[/tex] across all intervals. Therefore, Table B represents a linear function.
Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.