1. **State the problem:** We need to find the equation of a line given its x-intercept and y-intercept, then graph it. 2. **Recall the intercept form of a line:** The equation of a line with x-intercept $a$ and y-intercept $b$ is given by $$\frac{x}{a} + \frac{y}{b} = 1$$ 3. **Substitute the given intercepts:** Here, the x-intercept is $-9$ and the y-intercept is $5$, so $$\frac{x}{-9} + \frac{y}{5} = 1$$ 4. **Clear denominators by multiplying both sides by $-45$ (the least common multiple of $-9$ and $5$):** $$-45 \times \left(\frac{x}{-9} + \frac{y}{5}\right) = -45 \times 1$$ $$-45 \times \frac{x}{-9} + -45 \times \frac{y}{5} = -45$$ 5. **Simplify each term:** $$\cancel{-45} \times \frac{x}{\cancel{-9}} + \cancel{-45} \times \frac{y}{5} = -45$$ $$5x - 9y = -45$$ 6. **Rewrite the equation in slope-intercept form $y = mx + c$:** $$5x - 9y = -45$$ $$-9y = -45 - 5x$$ $$y = \frac{-45 - 5x}{-9}$$ $$y = \frac{-45}{-9} + \frac{-5x}{-9}$$ $$y = 5 + \frac{5}{9}x$$ 7. **Final equation:** $$y = \frac{5}{9}x + 5$$ This is the equation of the line with x-intercept $-9$ and y-intercept $5$.