Answer:
Explanation below
Step-by-step explanation:
Vertical Shift of Functions
Given a linear function
y = mx + b
The value of b is called the y-intercept or the y-coordinate where the line crosses the y-axis. If the function is shifted up by a value of k, then the new function is:
y' = mx + b + k
Similarily to shift the function down, the value of k is subtracted:
y''= mx + b - k
We are given the function:
[tex]\displaystyle y=\frac{2}{3}x+2[/tex]
1) To shift up the line, we select a value of k=10. The new shifted-up function is:
[tex]\displaystyle y=\frac{2}{3}x+2+10[/tex]
[tex]\displaystyle y=\frac{2}{3}x+12[/tex]
2) To shift down the line, we select a value of k=5. The new shifted-down function is:
[tex]\displaystyle y=\frac{2}{3}x+2-5[/tex]
[tex]\displaystyle y=\frac{2}{3}x-3[/tex]
3) To shift to the origin, we must select a specific value of k that cancels the y-intercept. We must shift down by k=2:
[tex]\displaystyle y=\frac{2}{3}x+2-2[/tex]
[tex]\displaystyle y=\frac{2}{3}x[/tex]
This new function has the y-intercept equal to 0
