1. **State the problem:** We need to choose the equation of the line shown in the graph. 2. **Use the slope-intercept form:** The formula for a line is $y=mx+b$, where $m$ is the slope and $b$ is the $y$-intercept. 3. **Read the graph values:** The line crosses the $y$-axis at $-2$, so $b=-2$. The line crosses the $x$-axis at $5$, so one point is $(5,0)$. 4. **Find the slope:** $$m=\frac{0-(-2)}{5-0}=\frac{2}{5}$$ So the slope is $\frac{2}{5}$. 5. **Write the equation:** Substitute $m=\frac{2}{5}$ and $b=-2$ into $y=mx+b$. $$y=\frac{2}{5}x-2$$ This is the same as $y=-2+\frac{2}{5}x$. 6. **Match the answer choice:** This matches **A**. **Final answer: A) $y=-2+\frac{2}{5}x$**