To find the equation of the line, we need to determine its slope and y-intercept. The equation of a line in slope-intercept form is:

$y = mx + b$

where $m$ is the slope and $b$ is the y-intercept.

1. Determine the y-intercept: From the graph, the line crosses the y-axis at $-2$, so $b = -2$.

2. Calculate the slope $m$: The slope is given by the rise over run (change in $y$ divided by change in $x$) between two points on the line.

   • From the graph, one point on the line is $(0, -2)$ and another point is $(5, 2)$.
   • The change in $y$ (rise) is $2 - (-2) = 4$.
   • The change in $x$ (run) is $5 - 0 = 5$.

   Therefore, the slope $m$ is:

   $m = \frac{4}{5}$

The equation of the line is:

$y = \frac{4}{5}x - 2$

Thus, the correct answer is A. $y = \frac{4}{5}x - 2$.

Would you like further explanation on finding the equation of a line or have other questions?

Here are five related questions:

1. How do you find the equation of a line given two points?
2. What is the significance of the slope in the equation of a line?
3. How does the y-intercept affect the position of a line on a graph?
4. How can you determine if two lines are parallel or perpendicular based on their slopes?
5. How would the equation change if the slope were negative?

Tip: When finding the slope, always ensure to take the difference in $y$-values (rise) over the difference in $x$-values (run) in the correct order, maintaining consistency between the two points.