We are given a graph and asked to identify which of the listed equations corresponds to the graphed line.

Let's analyze the graph:

• The line crosses the y-axis at $y = 2$, which suggests the y-intercept is 2.
• The slope of the line appears to be positive since the line rises as it moves from left to right.
• Counting the rise over run, we observe that the slope is $\frac{2}{3}$.

The equation of a line is generally expressed as $y = mx + b$, where:

• $m$ is the slope.
• $b$ is the y-intercept.

From the graph:

• Slope $m = \frac{2}{3}$.
• Y-intercept $b = 2$.

Thus, the equation of the line should be $y = \frac{2}{3}x + 2$, which matches option c).

Conclusion: The correct answer is c) $y = \frac{2}{3}x + 2$.

Do you want further details or have any questions?

Here are 5 related questions to deepen understanding:

1. How do you calculate the slope from a graph?
2. How would the graph change if the slope were negative?
3. What would the equation of the line be if the y-intercept were at $-3$ instead of $2$?
4. How does the standard form of a linear equation relate to the slope-intercept form?
5. What is the significance of the y-intercept in a linear equation?

Tip: Always check both the slope and the y-intercept when matching a graph to an equation.