To write the equation of the line in slope-intercept form (which is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept), we need to:

1. Find the slope (m): The slope is the ratio of the change in $y$ to the change in $x$ between two points on the line. From the graph, we can see that the line passes through two points: (3, -2) and (7, 6).

   The formula for slope is:

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

   Using the points (3, -2) and (7, 6):

   $m = \frac{6 - (-2)}{7 - 3} = \frac{6 + 2}{4} = \frac{8}{4} = 2$

   So, the slope $m = 2$.

2. Find the y-intercept (b): The y-intercept is the value of $y$ when $x = 0$. Looking at the graph, the line crosses the y-axis at $y = -8$. Therefore, the y-intercept $b = -8$.

3. Write the equation: Now that we have the slope and y-intercept, we can write the equation of the line:

   $y = 2x - 8$

This is the fully simplified equation of the line in slope-intercept form.

Would you like more details or have any questions? Here are some related questions you can explore:

1. How can you determine the slope of a line if only one point and the slope are given?
2. How do parallel lines relate in terms of slope?
3. What is the significance of the y-intercept in real-world applications?
4. How would the equation change if the slope were negative?
5. How can you convert a slope-intercept equation to standard form?

Tip: Remember, if the line passes through the origin (0, 0), the y-intercept will always be 0, making the equation simpler.