The equation provided is $y = -4x$. To determine if an ordered pair $(x, y)$ lies on the graph of this equation, substitute the $x$-coordinate into the equation and check if the resulting $y$-value matches the $y$-coordinate of the pair.

Verification of Each Ordered Pair:

1. (4, 0):
   Substituting $x = 4$:
   $y = -4(4) = -16$.
   Since $y \neq 0$, this pair is incorrect.

2. (2, 5):
   Substituting $x = 2$:
   $y = -4(2) = -8$.
   Since $y \neq 5$, this pair is incorrect.

3. (-1, 4):
   Substituting $x = -1$:
   $y = -4(-1) = 4$.
   Since $y = 4$, this pair is correct.

4. (5, -4):
   Substituting $x = 5$:
   $y = -4(5) = -20$.
   Since $y \neq -4$, this pair is incorrect.

5. (-4, -3):
   Substituting $x = -4$:
   $y = -4(-4) = 16$.
   Since $y \neq -3$, this pair is incorrect.

6. (-5, 5):
   Substituting $x = -5$:
   $y = -4(-5) = 20$.
   Since $y \neq 5$, this pair is incorrect.

Correct Ordered Pair:

The only correct pair is (-1, 4).

Would you like me to explain how to graph this equation or verify other points? Here are 5 related questions to explore further:

1. What does the slope of $-4$ represent in the equation $y = -4x$?
2. How do you determine if a point lies on a given linear equation?
3. What is the graph of $y = -4x$ and how is it oriented?
4. How can you write the equation of a line given its slope and a point?
5. If the slope changes to 2, what would the new equation look like?

Tip: The equation $y = -4x$ has a slope of $-4$, which means for every unit increase in $x$, $y$ decreases by 4 units.