Question

A point is translated on the coordinate plane from (4,-1) to (4,2). Journey writs 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 observe the change in the \( y \)-coordinate during the translation.

The initial \( y \)-coordinate is \( -1 \) and the final \( y \)-coordinate is \( 2 \).

The translation can be described as follows:
\[
g(-1) = 2
\]

We can substitute \( y = -1 \) into the function \( g(y) \):
\[
g(-1) = -1 + k
\]
Setting this equal to the final \( y \)-value:
\[
-1 + k = 2
\]
Now, we can solve for \( k \):
\[
k = 2 + 1 = 3
\]

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