Question

Brainliest pleasee?????

Answer 1

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:

$\displaystyle y=\frac{2}{3}x+2$

1) To shift up the line, we select a value of k=10. The new shifted-up function is:

$\displaystyle y=\frac{2}{3}x+2+10$

$\displaystyle y=\frac{2}{3}x+12$

2) To shift down the line, we select a value of k=5. The new shifted-down function is:

$\displaystyle y=\frac{2}{3}x+2-5$

$\displaystyle y=\frac{2}{3}x-3$

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:

$\displaystyle y=\frac{2}{3}x+2-2$

$\displaystyle y=\frac{2}{3}x$

This new function has the y-intercept equal to 0