Question

A) A point is translated on the coordinate plane from to . Journey writes the function
to describe the translation. What is the value of k? (1 point)
(4, −1) (4, 2)
g (y) = y + k
0
3
−5
−3

Answer 1

To find the value of \( k \) in the function \( g(y) = y + k \) that describes the translation of the point from \( (4, -1) \) to \( (4, 2) \), we can follow these steps:

1. Identify the y-coordinates of the starting point and the ending point:
- Starting point y-coordinate: \( -1 \)
- Ending point y-coordinate: \( 2 \)

2. The translation in the y-direction can be described by the equation:
\[
\text{End y-coordinate} = \text{Start y-coordinate} + k
\]

Plugging the values into this equation gives:
\[
2 = -1 + k
\]

3. Solve for \( k \):
\[
k = 2 + 1 = 3
\]

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