1. **State the problem.** We need to choose the equation of a line that crosses the y-axis at $-2$ and the x-axis at $5$. 2. **Use the slope-intercept form.** The formula for a line is $y=mx+b$. Here, $m$ is the slope and $b$ is the y-intercept. 3. **Find the slope from the graph.** The line goes through the points $(0,-2)$ and $(5,0)$. Use the slope formula: $$m=\frac{y_2-y_1}{x_2-x_1}$$ Substitute the points: $$m=\frac{0-(-2)}{5-0}=\frac{2}{5}$$ There is no fraction to cancel further, so the slope is $\frac{2}{5}$. 4. **Write the equation.** Now use $y=mx+b$ with $m=\frac{2}{5}$ and $b=-2$: $$y=\frac{2}{5}x-2$$ This is the same as $y=-2+\frac{2}{5}x$. 5. **Match the answer choice.** That matches choice A. **Final answer: A) $y=-2+\frac{2}{5}x$**