To determine the equation of the line in slope-intercept form, $y = mx + b$, let's extract the slope ($m$) and $y$-intercept ($b$) from the graph.

1. Identify the slope ($m$):

   • The slope is calculated as the rise over the run ($m = \frac{\text{rise}}{\text{run}}$).
   • From the graph, the line passes through the points $(-3, -2)$ and $(3, 2)$.
   • Calculate the slope: $m = \frac{\text{change in } y}{\text{change in } x} = \frac{2 - (-2)}{3 - (-3)} = \frac{4}{6} = \frac{2}{3}.$

2. Determine the $y$-intercept ($b$):

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

3. Write the equation: Substituting $m = \frac{2}{3}$ and $b = 0$ into the slope-intercept form: $y = \frac{2}{3}x + 0 \quad \text{or simply} \quad y = \frac{2}{3}x.$

Final Answer:

The equation of the line is: $y = \frac{2}{3}x$

Would you like me to provide additional details or verify the slope and intercept further? Let me know!

5 Questions to Explore Further:

1. How would the equation change if the $y$-intercept were nonzero?
2. Can you find the equation of a line parallel to this one passing through another point?
3. How do you calculate the equation of a perpendicular line to this one?
4. What is the significance of the slope in real-world applications?
5. How would the graph change if the slope were negative?

Tip: Always identify two clear points on the graph to calculate the slope accurately!