Question

A point is translated on the coordinate plane from (4,−1)
to (4,2)
. Journey writes the function g(y)=y+k
to describe the translation. What is the value of k?(1 point)
Responses

3
3

−5
negative 5

−3
negative 3

0

Answer 1

To determine the value of \( k \) in the function \( g(y) = y + k \) that describes the translation from the point \( (4, -1) \) to \( (4, 2) \), we need to analyze how the y-coordinate changes.

The original y-coordinate is \( -1 \) and the new y-coordinate is \( 2 \). The change in the y-coordinate can be calculated as follows:

\[
2 - (-1) = 2 + 1 = 3
\]

Since the function \( g(y) = y + k \) must account for this change, we can set up the equation:

\[
g(-1) = -1 + k = 2
\]

Now, we can solve for \( k \):

\[
-1 + k = 2 \\
k = 2 + 1 \\
k = 3
\]

Therefore, the value of \( k \) is \( 3 \).

The correct answer is:

**3**