Graph Equation 032B28

1. **State the problem:** We need to identify which graph corresponds to the equation $$2x - 10y = 40$$. 2. **Rewrite the equation in slope-intercept form:** To understand the graph, solve for $y$: $$2x - 10y = 40$$ Subtract $2x$ from both sides: $$-10y = -2x + 40$$ Divide both sides by $-10$: $$y = \frac{-2x + 40}{-10} = \frac{-2x}{-10} + \frac{40}{-10} = \frac{2}{10}x - 4 = \frac{1}{5}x - 4$$ 3. **Interpret the slope and intercepts:** - Slope $m = \frac{1}{5}$ (a small positive slope) - Y-intercept $b = -4$ 4. **Find the x-intercept:** Set $y=0$: $$0 = \frac{1}{5}x - 4$$ Add $4$ to both sides: $$\frac{1}{5}x = 4$$ Multiply both sides by $5$: $$x = 20$$ 5. **Summary:** The line has a small positive slope, crosses the y-axis at $-4$, and crosses the x-axis at $20$. 6. **Match with the graphs:** - Graph A: small positive slope, y-intercept about $4$, x-intercept about $-20$ (does not match) - Graph B: steep positive slope, y-intercept near $20$, x-intercept near $-2$ (does not match) - Graph C: small negative slope, y-intercept about $-4$, x-intercept about $-20$ (slope sign and x-intercept do not match) - Graph D: small positive slope, y-intercept about $-6$, x-intercept about $18$ (closest to our values) 7. **Conclusion:** Graph D best represents the equation $2x - 10y = 40$ because it has a small positive slope and intercepts close to $y=-4$ and $x=20$. **Final answer:** Graph D.