Let's analyze the table and derive the equation.

The given data in the table is as follows:

• For $x = 0$, $y = 0$
• For $x = 1$, $y = 3$
• For $x = 2$, $y = 6$
• For $x = 3$, $y = 9$
• For $x = 4$, $y = 12$

Step 1: Identify the Pattern

From the table, as $x$ increases by 1, $y$ increases by 3. This suggests a linear relationship of the form: $y = mx$ where $m$ is the slope.

Step 2: Calculate the Slope

Since $y$ increases by 3 for each increase of 1 in $x$, the slope $m = 3$.

Step 3: Write the Equation

The equation that models this relationship is: $y = 3x$

Conclusion

The correct answer is: $y = 3x$

Would you like further explanation on how to determine slopes or linear equations?

Here are five related questions to explore:

1. How would you determine the slope if the values in the table were not evenly spaced?
2. What would the equation look like if there were a constant added to $y = 3x$?
3. How can you tell if a table represents a linear or nonlinear relationship?
4. What is the significance of the slope in a linear equation?
5. How would the graph of $y = 3x$ look compared to $y = \frac{1}{3}x$?

Tip: In linear equations, the slope $m$ represents the rate of change, indicating how much $y$ changes for each unit increase in $x$.