The question is asking which points from the given options lie on the graph of the equation $y = -3x + 2$. We will substitute the $x$-coordinates of each point into the equation and check if the corresponding $y$-coordinates match.

Equation: $y = -3x + 2$

a) $(-1, 5)$

Substitute $x = -1$ into the equation: $y = -3(-1) + 2 = 3 + 2 = 5$ This matches the given $y$-coordinate. So, point $(-1, 5)$ lies on the graph.

b) $(0, 2)$

Substitute $x = 0$ into the equation: $y = -3(0) + 2 = 0 + 2 = 2$ This matches the given $y$-coordinate. So, point $(0, 2)$ lies on the graph.

c) $(2, -5)$

Substitute $x = 2$ into the equation: $y = -3(2) + 2 = -6 + 2 = -4$ This does not match the given $y$-coordinate (which is $-5$). Therefore, point $(2, -5)$ does not lie on the graph.

Conclusion:

Points $(-1, 5)$ and $(0, 2)$ lie on the graph of $y = -3x + 2$.

Do you want more details or have any questions?

Here are 5 related questions you can consider:

1. What is the slope of the line $y = -3x + 2$?
2. How do you find the y-intercept from a linear equation?
3. Can two points determine a unique line? Why or why not?
4. What would the equation of a line be if it was parallel to $y = -3x + 2$?
5. How can you graph $y = -3x + 2$ using its slope and intercept?

Tip: To check if a point lies on a graph, always substitute the coordinates into the equation and verify the results.