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 3 3 0 0 −3
Answers
GPT-4o mini
To determine the value of \( k \) in the function \( g(y) = y + k \) that describes the translation from the point \( (4, -1) \) to the point \( (4, 2) \), we can analyze how the \( y \)-coordinate is changing.
The initial \( y \)-coordinate is \(-1\), and the final \( y \)-coordinate is \(2\). Thus, we can set up the equation based on the transformation of \( y \):
\[
g(-1) = 2
\]
Substituting \(-1\) into the function gives:
\[
-1 + k = 2
\]
To find \( k \), we can solve for it:
\[
k = 2 + 1
\]
\[
k = 3
\]
Therefore, the value of \( k \) is \( 3 \).
So, the correct response is \( 3 \).
The initial \( y \)-coordinate is \(-1\), and the final \( y \)-coordinate is \(2\). Thus, we can set up the equation based on the transformation of \( y \):
\[
g(-1) = 2
\]
Substituting \(-1\) into the function gives:
\[
-1 + k = 2
\]
To find \( k \), we can solve for it:
\[
k = 2 + 1
\]
\[
k = 3
\]
Therefore, the value of \( k \) is \( 3 \).
So, the correct response is \( 3 \).