1. **State the problem:** We are given the equation $$\frac{x}{5} + \frac{y}{2} = 1$$ and asked to analyze it. 2. **Rewrite the equation:** To better understand the line, multiply both sides by 10 (the least common multiple of 5 and 2) to clear denominators: $$10 \times \left(\frac{x}{5} + \frac{y}{2}\right) = 10 \times 1$$ $$2x + 5y = 10$$ 3. **Find intercepts:** - To find the x-intercept, set $$y=0$$: $$2x + 5 \times 0 = 10 \Rightarrow 2x = 10 \Rightarrow x = 5$$ - To find the y-intercept, set $$x=0$$: $$2 \times 0 + 5y = 10 \Rightarrow 5y = 10 \Rightarrow y = 2$$ 4. **Rewrite in slope-intercept form:** Solve for $$y$$: $$2x + 5y = 10$$ $$5y = 10 - 2x$$ $$y = \frac{10 - 2x}{5} = 2 - \frac{2}{5}x$$ 5. **Interpretation:** The line crosses the x-axis at (5,0) and the y-axis at (0,2). The slope is $$-\frac{2}{5}$$, meaning the line falls as $$x$$ increases. **Final answer:** The line equation is $$y = 2 - \frac{2}{5}x$$ with intercepts at (5,0) and (0,2).