From the graph, we can see the line passing through points such as $(-4, 8)$, $(-2, 3)$, $(0, -2)$, and $(2, -7)$. To find the correct equation of this line in slope-intercept form $y = mx + b$, we need to determine the slope ($m$) and the y-intercept ($b$).

Step 1: Calculate the slope ($m$)

The formula for the slope between two points $(x_1, y_1)$ and $(x_2, y_2)$ is:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

We can use any two points from the graph. Let's take $(-4, 8)$ and $(0, -2)$.

$m = \frac{-2 - 8}{0 - (-4)} = \frac{-10}{4} = -\frac{5}{2}$

So the slope of the line is $-\frac{5}{2}$.

Step 2: Find the y-intercept ($b$)

The y-intercept is where the line crosses the y-axis, which is at the point $(0, -2)$. So the y-intercept $b$ is $-2$.

Step 3: Write the equation

Now that we know the slope is $-\frac{5}{2}$ and the y-intercept is $-2$, the equation of the line is:

$y = -\frac{5}{2}x - 2$

Conclusion

The correct equation of the line is:

$y = -\frac{5}{2}x - 2$

So the correct answer is the second option: $y = -\frac{5}{2}x - 2$.

Let me know if you'd like further clarification or have any more questions!

Here are some related questions for further exploration:

1. How do you find the slope of a line from its graph?
2. How can you identify the y-intercept of a line on a graph?
3. How would the equation change if the slope were positive instead of negative?
4. How do you graph a line when you know the slope and y-intercept?
5. What are the differences between slope-intercept form and point-slope form?

Tip: When identifying the slope from a graph, make sure to count the rise and run between two points to determine the correct ratio.