1. **State the problem:** We are given the linear equation $$2x - 3y + 24 = 0$$ and several points. We want to check which points lie on this line. 2. **Formula and rule:** A point $ (x, y) $ lies on the line if substituting $x$ and $y$ into the equation satisfies it, i.e., $$2x - 3y + 24 = 0$$ 3. **Check each point:** - For $(-6, 4)$: $$2(-6) - 3(4) + 24 = -12 - 12 + 24 = 0$$ Point lies on the line. - For $(6, 4)$: $$2(6) - 3(4) + 24 = 12 - 12 + 24 = 24 \neq 0$$ Point does not lie on the line. - For $(0, 8)$: $$2(0) - 3(8) + 24 = 0 - 24 + 24 = 0$$ Point lies on the line. - For $(8, 0)$: $$2(8) - 3(0) + 24 = 16 + 0 + 24 = 40 \neq 0$$ Point does not lie on the line. - For $(0, -8)$: $$2(0) - 3(-8) + 24 = 0 + 24 + 24 = 48 \neq 0$$ Point does not lie on the line. **Final answer:** Points $(-6,4)$ and $(0,8)$ lie on the line $2x - 3y + 24 = 0$.