lizziefufu2
Answered

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If [tex]$y = 12x - 7$[/tex] were changed to [tex]$y = 12x + 1$[/tex], how would the graph of the new function compare with the original?

A. It would be less steep.
B. It would be shifted down.
C. It would be steeper.
D. It would be shifted up.

Sagot :

GinnyAnswer
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.
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