1. **State the problem:** We are given the linear equation $$-2x + 5y = 20$$ and want to understand its graph and intercepts. 2. **Rewrite the equation to slope-intercept form:** Solve for $y$ to express the equation as $y = mx + b$ where $m$ is the slope and $b$ is the y-intercept. $$-2x + 5y = 20$$ Add $2x$ to both sides: $$\cancel{-2x} + 5y = 20 + \cancel{2x}$$ $$5y = 2x + 20$$ Divide both sides by 5: $$\frac{5y}{\cancel{5}} = \frac{2x + 20}{\cancel{5}}$$ $$y = \frac{2}{5}x + 4$$ 3. **Interpret the slope and intercept:** The slope $m = \frac{2}{5}$ means the line rises 2 units for every 5 units it moves right. The y-intercept $b = 4$ means the line crosses the y-axis at $(0,4)$. 4. **Find the x-intercept:** Set $y=0$ and solve for $x$: $$-2x + 5(0) = 20$$ $$-2x = 20$$ Divide both sides by $-2$: $$\frac{-2x}{\cancel{-2}} = \frac{20}{\cancel{-2}}$$ $$x = -10$$ So the x-intercept is at $(-10, 0)$. 5. **Summary:** The line crosses the y-axis at $(0,4)$ and the x-axis at $(-10,0)$, with slope $\frac{2}{5}$. The graph is a straight line with equation $$y = \frac{2}{5}x + 4$$. **Final answer:** $$y = \frac{2}{5}x + 4$$ Intercepts: $x = -10$, $y = 4$.