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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?

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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 \( x \).

Learn how to find the linear equation for a table of values. Given a table where x increases by 1 and y increases by 3, the solution explains the use of slope to determine the equation y = 3x. Ideal for students in Grades 6-8 exploring linear equations.

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