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)%0D%0AResponses%0D%0A%0D%0A−3%0D%0Anegative 3%0D%0A%0D%0A−5%0D%0Anegative 5%0D%0A%0D%0A0%0D%0A0%0D%0A%0D%0A3
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 (4, 2), we first need to analyze the translation in the y-coordinate.
The initial point has a y-coordinate of -1. After the translation, the new y-coordinate becomes 2.
The change in the y-coordinate due to the translation can be calculated as follows:
\[
\text{New y-coordinate} - \text{Old y-coordinate} = 2 - (-1) = 2 + 1 = 3.
\]
This means that the translation involves adding 3 to the initial y-coordinate.
In the function \( g(y) = y + k \), to find \( k \) such that when \( y = -1 \) we get the new coordinate 2:
\[
g(-1) = -1 + k = 2.
\]
Solving for \( k \):
\[
-1 + k = 2 \implies k = 2 + 1 = 3.
\]
Therefore, the value of \( k \) is \( 3 \).
The answer is:
\[
3.
\]
The initial point has a y-coordinate of -1. After the translation, the new y-coordinate becomes 2.
The change in the y-coordinate due to the translation can be calculated as follows:
\[
\text{New y-coordinate} - \text{Old y-coordinate} = 2 - (-1) = 2 + 1 = 3.
\]
This means that the translation involves adding 3 to the initial y-coordinate.
In the function \( g(y) = y + k \), to find \( k \) such that when \( y = -1 \) we get the new coordinate 2:
\[
g(-1) = -1 + k = 2.
\]
Solving for \( k \):
\[
-1 + k = 2 \implies k = 2 + 1 = 3.
\]
Therefore, the value of \( k \) is \( 3 \).
The answer is:
\[
3.
\]