Transformation Descriptions:

a. The slope is increased or decreased while the y-intercept is held constant:

• This represents a rotation about the y-intercept. Changing the slope tilts the line either clockwise or counterclockwise around the fixed y-intercept.

b. The y-intercept is decreased while the slope is held constant:

• This represents a translation downward (parallel shift). The line moves vertically while maintaining its slope and direction.

c. The slope $m$ is changed to $-m$:

• This represents a reflection across the y-axis. The direction of the line reverses, flipping it symmetrically.

d. The y-intercept is increased while the slope is held constant:

• This represents a translation upward (parallel shift). The line moves vertically while maintaining its slope and direction.

---

Would you like detailed graphical examples or further clarifications? Here are five related questions to explore:

1. How would a line's equation look after a rotation about a specific point instead of the y-intercept?
2. What happens when both slope and y-intercept change simultaneously?
3. Can you describe the transformation if the slope and y-intercept change by the same proportional factor?
4. How does reflection change if the line is reflected across the x-axis instead of the y-axis?
5. What is the geometric impact of modifying both the slope and y-intercept by opposite signs?

Tip: Always consider the fixed points or axes when describing transformations to understand their geometric effects fully.