To determine the transformation that occurs when moving from the graph of [tex]\( y = x \)[/tex] to the graph of [tex]\( y = x + 9.5 \)[/tex], follow these steps:
1. Analyze the Parent Function: The parent function here is [tex]\( y = x \)[/tex], which is a simple linear function passing through the origin with a slope of 1.
2. Identify the Transformation:
- The equation [tex]\( y = x + 9.5 \)[/tex] indicates that we have [tex]\( y = x \)[/tex] with an additional constant term, [tex]\( +9.5 \)[/tex].
3. Understand the Effect of the Constant Term:
- Adding a constant term to a function [tex]\( y = x \)[/tex] results in a vertical shift.
- Specifically, the addition of 9.5 to the function [tex]\( y = x \)[/tex] shifts the graph of the line vertically upwards.
4. Conclude the Transformation:
- Since the term added is [tex]\( +9.5 \)[/tex], this means that each point on the line [tex]\( y = x \)[/tex] is moved [tex]\( 9.5 \)[/tex] units upwards.
Therefore, the correct statement describing the graph of [tex]\( y = x + 9.5 \)[/tex] is that it represents a translation transformation where the graph of [tex]\( y = x \)[/tex] is shifted 9.5 units upwards.
