1. The problem asks us to determine which point does not lie on the graph of the line given by the equation $$y = -2x + 7$$. 2. To check if a point $ (x, y) $ lies on the graph, substitute the $x$-value into the equation and see if the resulting $y$ matches the point's $y$-value. 3. Check point a) $(-1, 9)$: Substitute $x = -1$ into the equation: $$y = -2(-1) + 7 = 2 + 7 = 9$$ The $y$-value matches, so point a) lies on the graph. 4. Check point b) $(4, -1)$: Substitute $x = 4$: $$y = -2(4) + 7 = -8 + 7 = -1$$ The $y$-value matches, so point b) lies on the graph. 5. Check point c) $(-3, 1)$: Substitute $x = -3$: $$y = -2(-3) + 7 = 6 + 7 = 13$$ The $y$-value is 13, but the point's $y$ is 1, so point c) does not lie on the graph. 6. Check point d) $(-2, 11)$: Substitute $x = -2$: $$y = -2(-2) + 7 = 4 + 7 = 11$$ The $y$-value matches, so point d) lies on the graph. Final answer: The point that does not lie on the graph is c) $(-3, 1)$.