https://file.aiquickdraw.com/mathbot/file/1726623636449jmnnqh1m.jpg

The given equation is \( y = \frac{1}{3}x + 2 \), which represents a linear function in slope-intercept form, \( y = mx + b \), where:
- \( m = \frac{1}{3} \) is the slope, meaning the line rises by 1 unit for every 3 units it moves to the right.
- \( b = 2 \) is the y-intercept, which is the point where the line crosses the y-axis at \( y = 2 \).

Now, we need to determine which graph matches this description:
1. The line should cross the y-axis at \( (0, 2) \).
2. The slope should rise 1 unit vertically for every 3 units horizontally (positive slope).

### Analysis of the options:
- **Option A**: The line crosses the y-axis at \( y = 2 \) and has a positive slope. This is the correct graph.
- **Option B**: The line has a negative slope, so it doesn't match.
- **Option C**: The line has a much steeper slope than \( \frac{1}{3} \), and its intercept is incorrect.
- **Option D**: The line has a negative slope and a different y-intercept, so it's also incorrect.

### Conclusion:
The correct graph is **A**.

Would you like more details or have any other questions?

Here are some related questions:
1. How do you find the slope of a line from two points on a graph?
2. What is the significance of the y-intercept in a linear equation?
3. How do you identify a positive versus negative slope just by looking at a graph?
4. How can you convert an equation from standard form to slope-intercept form?
5. What are the steps to graph a linear equation by plotting points?

**Tip**: Always check the y-intercept first when matching linear equations to their graphs.

¿Cuál gráfica representa la ecuación y = (1/3)x + 2?

Discover how to identify the correct graph for the linear equation y = (1/3)x + 2 by analyzing slope and y-intercept. This problem covers graphing techniques and is suitable for students in Grades 8-10.

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