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)
0
03
0-3
0-5

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 \( (4, 2) \), we need to identify how the \( y \)-coordinate changes during the translation.

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

The translation can be described by the change in the \( y \)-coordinate:

\[
\text{Change} = \text{Final} - \text{Initial} = 2 - (-1) = 2 + 1 = 3
\]

Since the function \( g(y) \) translates the \( y \)-coordinate upwards by 3 units, the equation representing this translation will be:

\[
g(y) = y + 3
\]

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

So, the answer is \( \boxed{3} \).