1. **State the problem:** We need to graph the inequality $$-3x + 4y < 4$$ on the Cartesian plane with axes from -10 to 10. 2. **Rewrite the inequality in terms of $y$:** $$-3x + 4y < 4$$ Add $3x$ to both sides: $$4y < 3x + 4$$ Divide both sides by 4: $$y < \frac{3x + 4}{4}$$ Show cancellation: $$y < \cancel{\frac{1}{\cancel{4}}}(3x + 4)$$ 3. **Interpret the inequality:** The boundary line is $$y = \frac{3}{4}x + 1$$. Since the inequality is strict ($<$), the boundary line is dashed. 4. **Graphing steps:** - Plot the line $$y = \frac{3}{4}x + 1$$ as a dashed line. - Shade the region below the line because $$y < \frac{3}{4}x + 1$$. 5. **Summary:** The graph is the half-plane below the dashed line $$y = \frac{3}{4}x + 1$$ on the coordinate plane from -10 to 10 on both axes.