To find the equation of the line in slope-intercept form (which is $y = mx + b$), we need to determine the slope $m$ and the y-intercept $b$ from the graph.

Step 1: Identify Points on the Line

Looking at the graph, two points on the line appear to be:

1. $(-12, 9)$
2. $(0, -3)$ (this is also the y-intercept).

Step 2: Calculate the Slope $m$

The slope formula is: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Using points $(-12, 9)$ and $(0, -3)$: $m = \frac{-3 - 9}{0 - (-12)} = \frac{-12}{12} = -1$

Step 3: Write the Equation in Slope-Intercept Form

Since the y-intercept $b$ is at $(0, -3)$, we have $b = -3$.

Thus, the equation of the line is: $y = -x - 3$

Would you like more details on each step or have any questions?

Here are 5 additional questions to explore similar concepts:

1. How would the equation change if the line had a different slope?
2. What happens to the graph if the y-intercept is shifted up or down?
3. Can you determine the equation of a line parallel to this one?
4. How can you confirm the slope if only one point and the y-intercept are given?
5. What changes would reflect the line across the x-axis?

Tip: When finding the slope, always subtract coordinates in the same order to avoid errors.