Answered

IDNLearn.com provides a collaborative environment for finding accurate answers. Join our community to receive timely and reliable responses to your questions from knowledgeable professionals.

Which table represents a linear function?

\begin{tabular}{|c|c|}
\hline[tex]$x$[/tex] & [tex]$y$[/tex] \\
\hline 1 & 3 \\
\hline 2 & 6 \\
\hline 3 & 12 \\
\hline 4 & 24 \\
\hline
\end{tabular}

\begin{tabular}{|c|c|}
\hline[tex]$x$[/tex] & [tex]$y$[/tex] \\
\hline 1 & 2 \\
\hline 2 & 5 \\
\hline 3 & 9 \\
\hline 4 & 14 \\
\hline
\end{tabular}

\begin{tabular}{|c|c|}
\hline[tex]$x$[/tex] & [tex]$y$[/tex] \\
\hline 1 & -3 \\
\hline 2 & -5 \\
\hline 3 & -7 \\
\hline 4 & -9 \\
\hline
\end{tabular}

\begin{tabular}{|c|c|}
\hline[tex]$x$[/tex] & [tex]$y$[/tex] \\
\hline 1 & -2 \\
\hline 2 & -4 \\
\hline 3 & -2 \\
\hline 4 & 0 \\
\hline
\end{tabular}

Sagot :

GinnyAnsweridn
To determine which of the given tables represents a linear function, we need to examine the changes in \( y \) for each increment in \( x \). A linear function has a constant rate of change (slope), and this means the difference between consecutive \( y \) values should be the same.

We have four different tables of \( x \) and \( y \) values.

Let's analyze each table:

1. First Table:
[tex]\[ \begin{array}{|c|c|} \hline x & y \\ \hline 1 & 3 \\ \hline 2 & 6 \\ \hline 3 & 12 \\ \hline 4 & 24 \\ \hline \end{array} \][/tex]
Differences in \( y \) values:
[tex]\[ 6 - 3 = 3 \\ 12 - 6 = 6 \\ 24 - 12 = 12 \][/tex]
Since the differences are not constant, this does not represent a linear function.

2. Second Table:
[tex]\[ \begin{array}{|c|c|} \hline x & y \\ \hline 1 & 2 \\ \hline 2 & 5 \\ \hline 3 & 9 \\ \hline 4 & 14 \\ \hline \end{array} \][/tex]
Differences in \( y \) values:
[tex]\[ 5 - 2 = 3 \\ 9 - 5 = 4 \\ 14 - 9 = 5 \][/tex]
Since the differences are not constant, this does not represent a linear function.

3. Third Table:
[tex]\[ \begin{array}{|c|c|} \hline x & y \\ \hline 1 & -3 \\ \hline 2 & -5 \\ \hline 3 & -7 \\ \hline 4 & -9 \\ \hline \end{array} \][/tex]
Differences in \( y \) values:
[tex]\[ -5 - (-3) = -2 \\ -7 - (-5) = -2 \\ -9 - (-7) = -2 \][/tex]
Since the differences are constant (\(-2\)), this represents a linear function.

4. Fourth Table:
[tex]\[ \begin{array}{|c|c|} \hline x & y \\ \hline 1 & -2 \\ \hline 2 & -4 \\ \hline 3 & -2 \\ \hline 4 & 0 \\ \hline \end{array} \][/tex]
Differences in \( y \) values:
[tex]\[ -4 - (-2) = -2 \\ -2 - (-4) = 2 \\ 0 - (-2) = 2 \][/tex]
Since the differences are not constant, this does not represent a linear function.

Based on the above analysis, the only table that represents a linear function is the third table:
[tex]\[ \begin{array}{|c|c|} \hline x & y \\ \hline 1 & -3 \\ \hline 2 & -5 \\ \hline 3 & -7 \\ \hline 4 & -9 \\ \hline \end{array} \][/tex]
We appreciate your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. Trust IDNLearn.com for all your queries. We appreciate your visit and hope to assist you again soon.