1. **State the problem:** We need to find which points lie on the line passing through $(-2,8)$ and $(5,-20)$. 2. **Find the equation of the line:** The slope $m$ is given by $$m=\frac{y_2 - y_1}{x_2 - x_1} = \frac{-20 - 8}{5 - (-2)} = \frac{-28}{7} = -4.$$ 3. Use point-slope form with point $(-2,8)$: $$y - 8 = -4(x - (-2))$$ $$y - 8 = -4(x + 2)$$ $$y - 8 = -4x - 8$$ $$y = -4x - 8 + 8$$ $$y = -4x.$$ 4. **Check each point:** Substitute $x$ into $y = -4x$ and see if $y$ matches. - $(0,6)$: $y = -4(0) = 0 \neq 6$ no. - $(7,5)$: $y = -4(7) = -28 \neq 5$ no. - $(-3,12)$: $y = -4(-3) = 12$ yes. - $(-6,-2)$: $y = -4(-6) = 24 \neq -2$ no. - $(4,16)$: $y = -4(4) = -16 \neq 16$ no. - $(-1,4)$: $y = -4(-1) = 4$ yes. **Final answer:** The points $(-3,12)$ and $(-1,4)$ lie on the line.