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−5negative 50033−3
Answers
GPT-4o mini
To determine the value of \( k \) in the function \( g(y) = y + k \), we need to look at what the translation from the point \((4, -1)\) to \((4, 2)\) means in terms of the \( y \) coordinate.
The initial \( y \)-coordinate is \(-1\) and it is translated to \(2\). Therefore, we can find \( k \) by using the relationship:
\[
g(-1) = 2
\]
Plugging \(-1\) into the function:
\[
g(-1) = -1 + k
\]
Setting this equal to \( 2 \):
\[
-1 + k = 2
\]
Now solving for \( k \):
\[
k = 2 + 1 = 3
\]
Thus, the value of \( k \) is \( 3 \).
The answer is \(\boxed{3}\).
The initial \( y \)-coordinate is \(-1\) and it is translated to \(2\). Therefore, we can find \( k \) by using the relationship:
\[
g(-1) = 2
\]
Plugging \(-1\) into the function:
\[
g(-1) = -1 + k
\]
Setting this equal to \( 2 \):
\[
-1 + k = 2
\]
Now solving for \( k \):
\[
k = 2 + 1 = 3
\]
Thus, the value of \( k \) is \( 3 \).
The answer is \(\boxed{3}\).