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

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 the point \( (4, 2) \), we need to focus on the \( y \)-coordinates of these points.

When we translate the point from \( (4, -1) \) to \( (4, 2) \), the \( y \)-coordinate changes from \(-1\) to \(2\). The transformation can be described as follows:

\[
g(-1) = 2
\]

Using the function \( g(y) = y + k \), we substitute \( y = -1 \):

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

Setting this equal to \( 2 \):

\[
-1 + k = 2
\]

To solve for \( k \):

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

Thus, the value of \( k \) is \( \boxed{3} \).