1. **State the problem:** Graph the inequality $3x - 4y > 12$ using intercepts. 2. **Rewrite the inequality as an equation to find intercepts:** $$3x - 4y = 12$$ 3. **Find the x-intercept:** Set $y=0$ and solve for $x$. $$3x - 4(0) = 12 \implies 3x = 12 \implies x = 4$$ So the x-intercept is $(4,0)$. 4. **Find the y-intercept:** Set $x=0$ and solve for $y$. $$3(0) - 4y = 12 \implies -4y = 12 \implies y = -3$$ So the y-intercept is $(0,-3)$. 5. **Plot the intercepts:** Plot points $(4,0)$ and $(0,-3)$ on the coordinate plane. 6. **Draw the boundary line:** Draw the line through these points. Since the inequality is strict ($>$), the line is dashed. 7. **Determine which side to shade:** Pick a test point not on the line, e.g., $(0,0)$. Substitute into the inequality: $$3(0) - 4(0) > 12 \implies 0 > 12$$ This is false, so shade the side opposite to $(0,0)$. **Final answer:** The graph is the region above the dashed line through $(4,0)$ and $(0,-3)$.