To solve this, let's extract the relevant information from the graph.

1. Identify the Equation of the Line:

   • The graph shows a straight line, so we know its equation will be in the form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

2. Determine the Slope $m$:

   • The slope $m$ is calculated as the change in $y$ divided by the change in $x$ between two points on the line.
   • From the graph, the line passes through the points $(-4, 4)$ and $(2, -4)$. Using these points: $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-4 - 4}{2 - (-4)} = \frac{-8}{6} = -\frac{4}{3}$

3. Find the y-Intercept $b$:

   • The y-intercept is the value of $y$ when $x = 0$. From the graph, the y-intercept appears to be $b = 0$.

4. Form the Equation:

   • With the slope $m = -\frac{4}{3}$ and the y-intercept $b = 0$, the equation of the line is: $y = -\frac{4}{3}x$

Thus, the equation of the line in the graph is $y = -\frac{4}{3}x$.

Would you like further details or clarifications?

Here are five follow-up questions related to this problem:

1. How do you calculate the slope if given different points on the line?
2. Can you determine the x-intercept from this equation?
3. How would the equation change if the y-intercept were different?
4. What is the significance of the slope being negative in this graph?
5. How can you verify the equation of the line by substituting points?

Tip: When calculating the slope between two points, always ensure that you correctly label the coordinates to avoid sign errors in your calculations.