1. **State the problem:** We need to write the two inequalities that describe the unshaded region on the coordinate plane. 2. **Identify the lines:** - The solid line passes through points (-3, -3) and (1, 7). - The dashed line passes through points (-3, 6) and (6, -3). 3. **Find the equation of the solid line:** - Slope $m = \frac{7 - (-3)}{1 - (-3)} = \frac{10}{4} = 2.5$. - Using point-slope form with point (-3, -3): $$y - (-3) = 2.5(x - (-3))$$ $$y + 3 = 2.5(x + 3)$$ $$y = 2.5x + 7.5 - 3 = 2.5x + 4.5$$ 4. **Find the equation of the dashed line:** - Slope $m = \frac{-3 - 6}{6 - (-3)} = \frac{-9}{9} = -1$. - Using point-slope form with point (-3, 6): $$y - 6 = -1(x + 3)$$ $$y = -x - 3 + 6 = -x + 3$$ 5. **Determine inequalities for the unshaded region:** - The unshaded region is above the solid line, so: $$y \geq 2.5x + 4.5$$ - The unshaded region is below the dashed line, so: $$y \leq -x + 3$$ **Final answer:** $$y \geq 2.5x + 4.5$$ $$y \leq -x + 3$$