Let's analyze the given functions step-by-step to determine how the graph of the new function compares with the original one.
The original function is:
[tex]\[ y = 2x + 7 \][/tex]
This equation is in the slope-intercept form [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] represents the slope and [tex]\( b \)[/tex] represents the y-intercept.
For the original line:
- The slope [tex]\( m \)[/tex] is [tex]\( 2 \)[/tex].
- The y-intercept [tex]\( b \)[/tex] is [tex]\( 7 \)[/tex].
The new function is:
[tex]\[ y = \frac{1}{2}x + 7 \][/tex]
This is also in the slope-intercept form.
For the new line:
- The slope [tex]\( m \)[/tex] is [tex]\( \frac{1}{2} \)[/tex].
- The y-intercept [tex]\( b \)[/tex] remains [tex]\( 7 \)[/tex].
Now, let's compare the slopes of the two lines:
- The slope of the original line is [tex]\( 2 \)[/tex].
- The slope of the new line is [tex]\( \frac{1}{2} \)[/tex].
Since [tex]\( \frac{1}{2} \)[/tex] is less than [tex]\( 2 \)[/tex], it means that the new line will have a smaller slope. A smaller slope indicates that the new line is less steep compared to the original line.
Therefore, the graph of the new function [tex]\( y = \frac{1}{2}x + 7 \)[/tex] would be less steep than the graph of the original function [tex]\( y = 2x + 7 \)[/tex].
So, the correct answer is:
B. It would be less steep.
