1. The problem asks which point lies on the line given by the equation $$y = -x + 4$$. 2. To check if a point $ (x, y) $ lies on the line, substitute the $x$ and $y$ values into the equation and see if the equation holds true. 3. Check point A: $(2, 2)$ Substitute $x=2$ into the equation: $$y = -2 + 4 = 2$$ Since $y=2$ matches the point's $y$ value, point A lies on the line. 4. Check point B: $(0, 4)$ Substitute $x=0$: $$y = -0 + 4 = 4$$ Matches $y=4$, so point B also lies on the line. 5. Check point C: $(4, 4)$ Substitute $x=4$: $$y = -4 + 4 = 0$$ Does not match $y=4$, so point C does not lie on the line. 6. Check point D: $(1, 1)$ Substitute $x=1$: $$y = -1 + 4 = 3$$ Does not match $y=1$, so point D does not lie on the line. 7. Therefore, points A and B lie on the line $y = -x + 4$. Final answer: Points A $(2, 2)$ and B $(0, 4)$ lie on the line.