Let's analyze this step by step:
1. Understanding the Original Function:
The original function given is [tex]\( y = x + 5 \)[/tex]. This is a linear equation in slope-intercept form [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
- For [tex]\( y = x + 5 \)[/tex], the slope [tex]\( m \)[/tex] is 1, and the y-intercept [tex]\( b \)[/tex] is 5.
2. Understanding the New Function:
The new function given is [tex]\( y = x + 9 \)[/tex]. This is also in slope-intercept form.
- For [tex]\( y = x + 9 \)[/tex], the slope [tex]\( m \)[/tex] is still 1, but the y-intercept [tex]\( b \)[/tex] is now 9.
3. Comparing the Slopes:
Since both functions have a slope of 1, the steepness of their graphs is identical. This means Answer A is incorrect.
4. Finding the Vertical Shift:
Notice that the y-intercept of the first function is 5, and the y-intercept of the second function is 9. The difference between the y-intercepts is [tex]\( 9 - 5 = 4 \)[/tex].
5. Nature of the Shift:
Since the y-intercept has increased from 5 to 9, it indicates that the entire graph of the function [tex]\( y = x + 5 \)[/tex] has been moved vertically upwards by 4 units to obtain the new graph [tex]\( y = x + 9 \)[/tex].
6. Conclusion:
Therefore, the transformation from [tex]\( y = x + 5 \)[/tex] to [tex]\( y = x + 9 \)[/tex] is a vertical shift upwards by 4 units.
Thus, the correct answer is:
D. It would be shifted up.
