To analyze how the graph of the new function [tex]\( y = \frac{1}{2} x + 7 \)[/tex] compares with the original function [tex]\( y = 2x + 7 \)[/tex], we need to consider the slopes of both functions.
1. Identify the slopes:
- The original function [tex]\( y = 2x + 7 \)[/tex] has a slope of 2.
- The new function [tex]\( y = \frac{1}{2} x + 7 \)[/tex] has a slope of [tex]\(\frac{1}{2}\)[/tex].
2. Compare the slopes:
- The slope of 2 means that for each unit increase in [tex]\( x \)[/tex], [tex]\( y \)[/tex] increases by 2 units, which can be visualized as a steeper incline.
- The slope of [tex]\(\frac{1}{2}\)[/tex] means that for each unit increase in [tex]\( x \)[/tex], [tex]\( y \)[/tex] increases by only [tex]\(\frac{1}{2}\)[/tex] unit, indicating a less steep incline.
3. Difference in slopes:
- The difference between the new slope and the original slope is [tex]\( \frac{1}{2} - 2 = -1.5 \)[/tex].
Since the slope of the new line [tex]\( \frac{1}{2} \)[/tex] is less than the slope of the original line 2, the graph of the new function [tex]\( y = \frac{1}{2} x + 7 \)[/tex] is less steep compared to the original function [tex]\( y = 2x + 7 \)[/tex].
Therefore, the correct answer is:
D. It would be less steep.
