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

1. Finding the slope ($m$): The slope $m = \frac{\Delta y}{\Delta x}$ is the change in $y$ over the change in $x$. Using two points on the line:

   • Point 1: $(-8, -4)$
   • Point 2: $(-4, 2)$

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

   So, the slope is $m = \frac{3}{2}$.

2. Finding the y-intercept ($b$): The y-intercept is where the line crosses the $y$-axis. Observing the graph, the line crosses the $y$-axis at $b = 6$.

Thus, the equation of the line is:

$y = \frac{3}{2}x + 6$

Would you like a detailed explanation of how these steps were calculated, or do you have additional questions? Here are five related questions to consider:

1. How can we verify the slope by using other points on the line?
2. What would the equation look like if it were expressed in standard form?
3. How can the slope-intercept equation help determine other points on the line?
4. What does the slope tell us about the steepness of the line?
5. How do we find the equation of a line parallel or perpendicular to this one?

Tip: When determining the slope, always ensure you're using points exactly on the grid lines to avoid estimation errors.