Get the answers you need at Westonci.ca, where our expert community is always ready to help with accurate information. Get detailed and precise answers to your questions from a dedicated community of experts on our Q&A platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.
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]
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]
We appreciate your time. Please come back anytime for the latest information and answers to your questions. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.