Let's analyze the graph and the problem to identify which equation represents the line shown.

Step 1: Determine the slope of the line

We can calculate the slope ($m$) by selecting two points on the line. From the graph:

• Point 1: $(-6, 5)$
• Point 2: $(0, -3)$

The formula for the slope is: $m = \frac{y_2 - y_1}{x_2 - x_1}$

Substitute the coordinates of the two points: $m = \frac{-3 - 5}{0 - (-6)} = \frac{-8}{6} = -\frac{4}{3}$

Step 2: Identify the y-intercept

The y-intercept ($b$) is the point where the line crosses the y-axis. From the graph, the line crosses the y-axis at $(0, -3)$, so $b = -3$.

Step 3: Write the equation of the line

The general equation of a line is: $y = mx + b$

Substitute the slope $m = -\frac{4}{3}$ and the y-intercept $b = -3$: $y = -\frac{4}{3}x - 3$

However, none of the options directly match this equation. Let's compare each option:

• Option A: $y = -\frac{5}{3}x - 5$
• Option B: $y = -\frac{5}{3}x - 3$
• Option C: $y = -\frac{3}{5}x - 5$
• Option D: $y = -\frac{3}{5}x - 3$

None of the equations have the correct slope of $-\frac{4}{3}$, meaning the correct equation is not listed. Therefore, the answer cannot be chosen from the options provided.

Let me know if you have questions or would like more details.

Here are some related questions to explore:

1. How can you determine the slope of a line from a graph?
2. What is the significance of the y-intercept in a linear equation?
3. Can the slope of a line be positive and what does it mean graphically?
4. How can you rewrite the equation of a line in different forms (e.g., standard form)?
5. How would you calculate the slope if the graph were less clear?

Tip: Always check two points on the graph carefully to ensure the slope calculation is accurate.