To move the red point so that it lies on the line described by the equation $4x - y + 3 = 0$, we need to ensure the point satisfies this equation.

Here's the process:

1. Let the coordinates of the red point be $(x, y)$.
2. Substitute the value of $x$ from the red point into the equation $4x - y + 3 = 0$.
3. Solve for $y$ to find the corresponding coordinate that satisfies the equation.

For example, if the current $x$-coordinate of the red point is known, substitute it into $4x - y + 3 = 0$ to find the matching $y$-coordinate.

Would you like further details or examples on how to calculate specific coordinates for this line?

Here are five questions to explore related concepts:

1. How do you determine if a point lies on a given line?
2. What is the slope of the line $4x - y + 3 = 0$?
3. How can you graphically represent the line from its equation?
4. What are the x-intercept and y-intercept of this line?
5. How would you adjust the point's position if it doesn't initially lie on the line?

Tip: To check if a point lies on a line, substitute the point's coordinates into the equation and see if both sides are equal.