Final answer:
The transformation consists of reflecting a point first over the horizontal axis, making its y-coordinate negative, and then reflecting it over the line y=1, changing its y-coordinate based on the distance from y=1. Applied to a line with a specific slope and y-intercept, these transformations alter its position but not its slope.
Step-by-step explanation:
The transformation described involves two reflections: one across the horizontal axis (often referred to as the x-axis in coordinate geometry) and another reflection across the line where y equals 1. When a point is reflected over the horizontal axis, its y-coordinate changes sign, but its x-coordinate remains the same. For example, if we start with a point (x, y), after the reflection over the horizontal axis, it becomes (x, -y). Next, when we reflect a point across the line y=1, the y-coordinate changes based on its distance from the line y=1. For a point located at (x, y), after reflection across the line, it becomes (x, 2 - y).
These transformations can be applied to the line described in Figure A1, which has a slope (rise over run) of 3 and a y-intercept of 9. The equation of this line is y = 3x + 9. If we reflect this entire line first over the horizontal axis and then over the line y=1, we would get a new line with a slope still equal to -3, but with a different y-intercept, as the entire line has undergone these transformations.