1. **State the problem:** We need to find the equation of a line given its graph. 2. **Analyze the graph:** The line crosses the y-axis at $-2$ and the x-axis at $5$. 3. **Recall the slope-intercept form:** The equation of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. 4. **Identify the y-intercept:** From the graph, $b = -2$. 5. **Calculate the slope $m$:** The slope is the change in $y$ over the change in $x$ between two points. Points: $(0, -2)$ and $(5, 0)$. $$m = \frac{0 - (-2)}{5 - 0} = \frac{2}{5}$$ 6. **Write the equation:** Substitute $m = \frac{2}{5}$ and $b = -2$ into $y = mx + b$: $$y = \frac{2}{5}x - 2$$ 7. **Match with options:** This matches option A: $y = -2 + \frac{2}{5}x$. **Final answer:** $y = -2 + \frac{2}{5}x$