Which Table Shows Ordered Pairs That Satisfy The Function $y=\frac{3x}{2}$?A.$\[ \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline -1 & $-\frac{3}{2}$ \\ \hline 0 & 0 \\ \hline 1 & $\frac{3}{2}$

Which Table Shows Ordered Pairs that Satisfy the Function $y=\frac{3x}{2}$?

Understanding the Function

The given function is $y=\frac{3x}{2}$. This is a linear function, which means it represents a straight line when graphed on a coordinate plane. The function is in the form of $y=mx$, where $m$ is the slope of the line. In this case, the slope is $\frac{3}{2}$.

Ordered Pairs and Functions

An ordered pair is a pair of numbers that are written in the form $(x, y)$. In the context of functions, ordered pairs are used to represent the input and output values of the function. For example, if we have the function $y=x^2$, the ordered pair $(2, 4)$ represents the input value $x=2$ and the output value $y=4$.

Satisfying the Function

To satisfy the function $y=\frac{3x}{2}$, an ordered pair must have a $y$-value that is equal to $\frac{3x}{2}$, where $x$ is the $x$-value of the ordered pair. In other words, if we plug in a value of $x$ into the function, the resulting $y$-value must be equal to the $y$-value of the ordered pair.

Analyzing the Tables

We are given four tables to choose from, each containing ordered pairs. We need to determine which table shows ordered pairs that satisfy the function $y=\frac{3x}{2}$.

Table A

$x$	$y$
-1	$-\frac{3}{2}$
0	0
1	$\frac{3}{2}$

Table B

$x$	$y$
-1	1
0	0
1	1

Table C

$x$	$y$
-1	-1
0	0
1	1

Table D

$x$	$y$
-1	2
0	0
1	3

Evaluating the Tables

To determine which table shows ordered pairs that satisfy the function $y=\frac{3x}{2}$, we need to plug in the values of $x$ from each table into the function and see if the resulting $y$-values match the $y$-values in the table.

Table A

For $x=-1$, we have $y=\frac{3(-1)}{2}=-\frac{3}{2}$. This matches the $y$-value in Table A.

For $x=0$, we have $y=\frac{3(0)}{2}=0$. This matches the $y$-value in Table A.

For $x=1$, we have $y=\frac{3(1)}{2}=\frac{3}{2}$. This matches the $y$-value in Table A.

Table B

For $x=-1$, we have $y=\frac{3(-1)}{2}=-\frac{3}{2}$. This does not match the $y$-value in Table B.

For $x=0$, we have $y=\frac{3(0)}{2}=0$. This matches the $y$-value in Table B.

For $x=1$, we have $y=\frac{3(1)}{2}=\frac{3}{2}$. This does not match the $y$-value in Table B.

Table C

For $x=-1$, we have $y=\frac{3(-1)}{2}=-\frac{3}{2}$. This does not match the $y$-value in Table C.

For $x=0$, we have $y=\frac{3(0)}{2}=0$. This matches the $y$-value in Table C.

For $x=1$, we have $y=\frac{3(1)}{2}=\frac{3}{2}$. This does not match the $y$-value in Table C.

Table D

For $x=-1$, we have $y=\frac{3(-1)}{2}=-\frac{3}{2}$. This does not match the $y$-value in Table D.

For $x=0$, we have $y=\frac{3(0)}{2}=0$. This matches the $y$-value in Table D.

For $x=1$, we have $y=\frac{3(1)}{2}=\frac{3}{2}$. This does not match the $y$-value in Table D.

Conclusion

Based on our analysis, we can see that only Table A shows ordered pairs that satisfy the function $y=\frac{3x}{2}$. The ordered pairs in Table A have $y$-values that are equal to $\frac{3x}{2}$, where $x$ is the $x$-value of the ordered pair. Therefore, the correct answer is Table A.

Key Takeaways

• The function $y=\frac{3x}{2}$ represents a straight line with a slope of $\frac{3}{2}$.
• Ordered pairs are used to represent the input and output values of a function.
• To satisfy the function $y=\frac{3x}{2}$, an ordered pair must have a $y$-value that is equal to $\frac{3x}{2}$, where $x$ is the $x$-value of the ordered pair.
• We can use tables to represent ordered pairs and determine which table shows ordered pairs that satisfy a given function.
  Q&A: Understanding the Function $y=\frac{3x}{2}$

Frequently Asked Questions

We have received many questions about the function $y=\frac{3x}{2}$ and how to determine which table shows ordered pairs that satisfy this function. Below, we have answered some of the most frequently asked questions.

Q: What is the slope of the function $y=\frac{3x}{2}$?

A: The slope of the function $y=\frac{3x}{2}$ is $\frac{3}{2}$. This means that for every one unit increase in $x$, the value of $y$ increases by $\frac{3}{2}$ units.

Q: How do I determine which table shows ordered pairs that satisfy the function $y=\frac{3x}{2}$?

A: To determine which table shows ordered pairs that satisfy the function $y=\frac{3x}{2}$, you need to plug in the values of $x$ from each table into the function and see if the resulting $y$-values match the $y$-values in the table.

Q: What if the $y$-value in the table does not match the $y$-value I calculated using the function?

A: If the $y$-value in the table does not match the $y$-value you calculated using the function, then the table does not show ordered pairs that satisfy the function $y=\frac{3x}{2}$.

Q: Can I use any table to determine which ordered pairs satisfy the function $y=\frac{3x}{2}$?

A: No, you cannot use any table to determine which ordered pairs satisfy the function $y=\frac{3x}{2}$. The table must have ordered pairs that are in the form $(x, y)$, where $y$ is equal to $\frac{3x}{2}$.

Q: How do I know if an ordered pair satisfies the function $y=\frac{3x}{2}$?

A: To determine if an ordered pair satisfies the function $y=\frac{3x}{2}$, you need to plug in the value of $x$ from the ordered pair into the function and see if the resulting $y$-value matches the $y$-value in the ordered pair.

Q: Can I use a graph to determine which ordered pairs satisfy the function $y=\frac{3x}{2}$?

A: Yes, you can use a graph to determine which ordered pairs satisfy the function $y=\frac{3x}{2}$. If the ordered pair is on the graph, then it satisfies the function.

Q: How do I graph the function $y=\frac{3x}{2}$?

A: To graph the function $y=\frac{3x}{2}$, you can use a coordinate plane and plot points that satisfy the function. You can also use a graphing calculator or software to graph the function.

Q: Can I use a table to graph the function $y=\frac{3x}{2}$?

A: Yes, you can use a table to graph the function $y=\frac{3x}{2}$. You can create a table with values of $x$ and calculate the corresponding values of $y$ using the function. Then, you can plot the points on a coordinate plane to create a graph.

Conclusion

We hope that these questions and answers have helped you understand the function $y=\frac{3x}{2}$ and how to determine which table shows ordered pairs that satisfy this function. If you have any more questions, please don't hesitate to ask.

Key Takeaways

• The function $y=\frac{3x}{2}$ represents a straight line with a slope of $\frac{3}{2}$.
• Ordered pairs are used to represent the input and output values of a function.
• To determine which table shows ordered pairs that satisfy the function $y=\frac{3x}{2}$, you need to plug in the values of $x$ from each table into the function and see if the resulting $y$-values match the $y$-values in the table.
• You can use a graph to determine which ordered pairs satisfy the function $y=\frac{3x}{2}$.
• You can use a table to graph the function $y=\frac{3x}{2}$.

Additional Resources

If you want to learn more about the function $y=\frac{3x}{2}$ and how to determine which table shows ordered pairs that satisfy this function, we recommend checking out the following resources:

• Mathway: A math problem solver that can help you solve equations and inequalities.
• Khan Academy: A free online learning platform that offers video lessons and practice exercises on a variety of math topics.
• Wolfram Alpha: A computational knowledge engine that can help you solve math problems and provide information on a variety of topics.