1. **State the problem:** We need to graph the line given by the equation $$18x - 48y = 1440$$ using intercepts. 2. **Rewrite the equation:** Start by isolating $$y$$ to find the slope-intercept form. $$18x - 48y = 1440$$ Subtract $$18x$$ from both sides: $$-48y = -18x + 1440$$ Divide both sides by $$-48$$: $$y = \frac{-18x + 1440}{-48}$$ Show cancellation: $$y = \frac{\cancel{-18}x + \cancel{1440}}{\cancel{-48}} = \frac{18}{48}x - \frac{1440}{48}$$ Simplify the fractions: $$y = \frac{3}{8}x - 30$$ 3. **Find the intercepts:** - **x-intercept:** Set $$y=0$$ and solve for $$x$$. $$0 = \frac{3}{8}x - 30$$ Add 30 to both sides: $$30 = \frac{3}{8}x$$ Multiply both sides by $$\frac{8}{3}$$: $$x = 30 \times \frac{8}{3} = 80$$ - **y-intercept:** Set $$x=0$$ and solve for $$y$$. $$y = \frac{3}{8} \times 0 - 30 = -30$$ 4. **Interpretation:** The line crosses the x-axis at $$(80, 0)$$ and the y-axis at $$(0, -30)$$. 5. **Final answer:** The intercepts are $$x=80$$ and $$y=-30$$, which can be used to graph the line.