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.