To determine which function best represents the graph, we need to analyze the line’s slope and y-intercept.

Step 1: Identify the Slope

The slope of the line $m$ is the rise over the run. We can choose two points on the line:

• Point 1: $(-6, -6)$
• Point 2: $(6, 6)$

The slope $m$ is given by:

$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{6 - (-6)}{6 - (-6)} = \frac{12}{12} = 1$

So, the slope of the line is $m = 1$.

Step 2: Identify the Y-Intercept

The line crosses the y-axis at $y = 0$. This means the y-intercept $b = 0$.

Step 3: Equation of the Line

Using the slope-intercept form of a line $y = mx + b$, where $m = 1$ and $b = 0$, the equation of the line is:

$y = 1x + 0 \quad \text{or simply} \quad y = x$

Step 4: Compare with the Given Options

None of the options exactly match $y = x$. However, this suggests that none of the provided functions match the graph perfectly. Based on the available options, there might be a confusion, but let's check them:

• A: $y = \frac{3}{2}x - 4$ — the slope is $\frac{3}{2}$, which is not correct.
• B: $y = \frac{2}{3}x + 6$ — slope is $\frac{2}{3}$, incorrect.
• C: $y = \frac{3}{2}x + 6$ — incorrect slope.
• D: $y = \frac{2}{3}x - 4$ — incorrect slope.

None of these match the slope of the line. The graph should correspond to a line with a slope of 1 and a y-intercept of 0, which is not represented in the answer choices. You may need to check if the question options have any error or consider $y = x$ as the best-fit answer.

Let me know if you'd like more details or have any further questions. Here's a set of related questions:

1. How do you determine the slope from two points?
2. What does the y-intercept of a line represent?
3. How does the slope-intercept form of a line work?
4. Can you compare the differences between positive and negative slopes in graphs?
5. What are the characteristics of lines with a slope of 1?

Tip: Always verify the slope and y-intercept by testing a few points from the graph!