Graph Equation De87B9

1. **State the problem:** We need to identify which graph corresponds to the equation $$x - 2y = 30$$. 2. **Rewrite the equation in slope-intercept form:** To understand the graph, solve for $y$: $$x - 2y = 30$$ Subtract $x$ from both sides: $$-2y = 30 - x$$ Divide both sides by $-2$: $$y = \frac{30 - x}{-2} = \frac{30}{-2} - \frac{x}{-2} = -15 + \frac{x}{2}$$ Or equivalently: $$y = \frac{1}{2}x - 15$$ 3. **Interpret the slope and intercepts:** - The slope is $\frac{1}{2}$ (positive slope). - The y-intercept is $-15$. 4. **Find the x-intercept:** Set $y=0$: $$0 = \frac{1}{2}x - 15$$ Add $15$ to both sides: $$\frac{1}{2}x = 15$$ Multiply both sides by $2$: $$x = 30$$ So the x-intercept is at $30$. 5. **Match with the graph descriptions:** - Graph A: negative slope, x-intercept near $-30$, y-intercept near $-15$. - Graph B: positive slope, y-intercept near $-15$, x-intercept near $30$. - Graph C: positive slope, y-intercept near $15$, x-intercept near $-30$. - Graph D: steep positive slope, y-intercept near $30$, x-intercept near $-15$. 6. **Conclusion:** The equation has a positive slope $\frac{1}{2}$, y-intercept $-15$, and x-intercept $30$, which matches graph B. **Final answer:** Graph B represents the equation $x - 2y = 30$.