Given the function below, fill in the table of values and use the table values to graph.

[tex]y=3 x[/tex]

| x | y=3x |
|---|---|
| -3 | |
| -2 | |
| -1 | |
| 0 | |
| 1 | |
| 2 | |
| 3 | |

Calculate y for each x value using y = 3 x .
For x = − 3 , − 2 , − 1 , 0 , 1 , 2 , 3 , the corresponding y values are − 9 , − 6 , − 3 , 0 , 3 , 6 , 9 .
Plot the points ( − 3 , − 9 ) , ( − 2 , − 6 ) , ( − 1 , − 3 ) , ( 0 , 0 ) , ( 1 , 3 ) , ( 2 , 6 ) , ( 3 , 9 ) on a coordinate plane.
Draw a straight line through these points, representing the function y = 3 x . The final answer is the filled table and the graph of the line. The table is:




x
y = 3x



-3
-9


-2
-6


-1
-3


0
0


1
3


2
6


3
9


The graph is a straight line passing through the origin with a slope of 3.
Explanation

Understanding the Problem We are given the function y = 3 x and asked to fill in the table of values for x = − 3 , − 2 , − 1 , 0 , 1 , 2 , 3 . Then, we will use these values to graph the function.

Calculating y values Let's calculate the y values for each given x value using the function y = 3 x .

Calculating y for x = -3 For x = − 3 , we have y = 3 ( − 3 ) = − 9 .

Calculating y for x = -2 For x = − 2 , we have y = 3 ( − 2 ) = − 6 .

Calculating y for x = -1 For x = − 1 , we have y = 3 ( − 1 ) = − 3 .

Calculating y for x = 0 For x = 0 , we have y = 3 ( 0 ) = 0 .

Calculating y for x = 1 For x = 1 , we have y = 3 ( 1 ) = 3 .

Calculating y for x = 2 For x = 2 , we have y = 3 ( 2 ) = 6 .

Calculating y for x = 3 For x = 3 , we have y = 3 ( 3 ) = 9 .

Plotting the points and drawing the line Now we have the following points: ( − 3 , − 9 ) , ( − 2 , − 6 ) , ( − 1 , − 3 ) , ( 0 , 0 ) , ( 1 , 3 ) , ( 2 , 6 ) , ( 3 , 9 ) . We can plot these points on a coordinate plane and draw a line through them.

Final Answer The table of values is:





x
y = 3x



-3
-9


-2
-6


-1
-3


0
0


1
3


2
6


3
9


The graph is a straight line passing through the origin with a slope of 3.
Examples
Understanding linear functions like y = 3 x is crucial in many real-world scenarios. For instance, if you're saving money at a rate of 3 p er d a y , t h e f u n c t i o n y = 3x m o d e l syo u r t o t a l s a v in g s ( y ) a f t er x$ days. Similarly, if you're traveling at a constant speed of 3 miles per hour, this function represents the distance you've traveled after a certain number of hours. Recognizing and applying linear functions helps in making predictions and understanding relationships between quantities in everyday situations.

Answered by GinnyAnswer | 2025-07-08

We calculated the y values for the function y = 3 x across the given x values, resulting in a completed table. These values were plotted on a graph, forming a straight line that reflects the linear relationship. The table of values includes pairs such as (-3, -9) and (3, 9).
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Answered by Anonymous | 2025-07-09