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

−5
negative 5

0
0

−3
negative 3

3

Answer 1

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

The translation is only vertical, meaning the \( x \)-coordinate remains the same (4), while the \( y \)-coordinate changes from -1 to 2.

To describe this transformation using the function \( g(y) = y + k \):
- We can set \( y = -1 \) (the original \( y \)-coordinate).
- The transformed \( y \)-coordinate after translation should be \( 2 \).

Thus, we have:

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

Now, we solve for \( k \):

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

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

The answer is:

**3**