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

1. Y-intercept (b): Observing the graph, the line crosses the y-axis at $y = -3$. So, $b = -3$.

2. Slope (m): To find the slope, use two points on the line. We can see the points $(-6, -6)$ and $(0, -3)$ on the line.

   • Slope $m = \frac{\Delta y}{\Delta x} = \frac{-3 - (-6)}{0 - (-6)} = \frac{3}{6} = \frac{1}{2}$.

Thus, the equation of the line is: $y = \frac{1}{2}x - 3$

Would you like a more detailed explanation, or do you have any questions?

1. What is slope-intercept form?
2. How do you calculate the slope between two points?
3. Why is the y-intercept important in an equation?
4. What other forms can we use to represent linear equations?
5. How do we interpret positive vs. negative slopes?

Tip: Always choose clearly visible points on the line to accurately calculate the slope.