The problem is asking for the equation of the line $-x + 3y - 15 = 0$ after it has been rotated 90° clockwise about the origin $O(0,0)$.

Steps to solve:

1. Equation of the line: The given line is $-x + 3y - 15 = 0$, which can be written as $y = \frac{1}{3}x + 5$.

2. General rotation formula: To rotate a line, we use the parametric point rotation formulas. For a 90° clockwise rotation about the origin, the transformation of any point $(x, y)$ is: $(x', y') = (y, -x)$ This means every point on the line $(x, y)$ will map to a new point $(y, -x)$.

3. Transforming the equation: To rotate the entire line, we substitute $x' = y$ and $y' = -x$ into the original equation $-x + 3y - 15 = 0$.

   Substituting these transformations: $-(y') + 3(-x') - 15 = 0$ Simplifying: $-y' - 3x' - 15 = 0$ This is the equation of the rotated line.

4. Final equation: Therefore, the equation of the line after a 90° clockwise rotation is: $-y - 3x - 15 = 0 \quad \text{or equivalently} \quad 3x + y + 15 = 0$

Would you like more details on the steps?

Here are 5 related questions you might want to explore:

1. What is the effect of a 90° counterclockwise rotation on the same line?
2. How would you rotate a line by 180° around the origin?
3. Can the general formula for any angle of rotation be applied here?
4. What is the geometric interpretation of rotating a line?
5. How would you graph the original line and the rotated line?

Tip: When rotating figures or equations, always use transformation formulas specific to the rotation angle and direction.