To understand how the graph of the new function [tex]\( y = 12x \)[/tex] compares with the original function [tex]\( y = 12x - 2 \)[/tex], let's analyze the given functions step-by-step.
1. Original Equation [tex]\( y = 12x - 2 \)[/tex]:
- This is a linear equation of the form [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
- For [tex]\( y = 12x - 2 \)[/tex]:
- The slope [tex]\( m \)[/tex] is 12.
- The y-intercept [tex]\( b \)[/tex] is -2.
- This means the line crosses the y-axis at [tex]\( (0, -2) \)[/tex] and has a steepness determined by the slope of 12.
2. New Equation [tex]\( y = 12x \)[/tex]:
- This is also a linear equation of the form [tex]\( y = mx + b \)[/tex].
- For [tex]\( y = 12x \)[/tex]:
- The slope [tex]\( m \)[/tex] remains 12.
- The y-intercept [tex]\( b \)[/tex] is now 0.
- This means the line crosses the y-axis at [tex]\( (0, 0) \)[/tex] and maintains the same steepness as before (slope of 12).
3. Comparison:
- Since the slope (12) in both equations is the same, the steepness of the graph does not change.
- The main difference is the y-intercept.
- The y-intercept in the original equation is -2.
- The y-intercept in the new equation is 0.
4. Conclusion:
- The change in the y-intercept from -2 to 0 means that the entire graph is shifted vertically.
- Since 0 is greater than -2, the shift is upwards.
Thus, the correct choice is:
A. It would be shifted up.
