To compare the graphs of the original function [tex]\( y = 12x - 7 \)[/tex] with the new function [tex]\( y = 12x + 1 \)[/tex], we need to examine their slopes and y-intercepts:
1. Examine the slopes:
- The slope of the original function [tex]\( y = 12x - 7 \)[/tex] is [tex]\( 12 \)[/tex].
- The slope of the new function [tex]\( y = 12x + 1 \)[/tex] is also [tex]\( 12 \)[/tex].
Since both functions have the same slope, they are equally steep. Therefore, options A and C are incorrect because the steepness does not change.
2. Examine the y-intercepts:
- The y-intercept of the original function is [tex]\( -7 \)[/tex].
- The y-intercept of the new function is [tex]\( +1 \)[/tex].
The change in the y-intercept from [tex]\( -7 \)[/tex] to [tex]\( +1 \)[/tex] indicates a vertical shift. Since the new y-intercept [tex]\( +1 \)[/tex] is greater than the original y-intercept [tex]\( -7 \)[/tex], the graph of the new function shifts upward.
Therefore, the correct answer is:
D. It would be shifted up.
