Question

A point is translated on the coordinate plane from (5, -3) to (5,7). Journey write 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 of the point from \( (5, -3) \) to \( (5, 7) \), we need to analyze how the \( y \)-coordinate changes during the translation.

The initial \( y \)-coordinate is \( -3 \), and after the translation, the \( y \)-coordinate is \( 7 \).

This means:

\[
g(-3) = 7
\]

Substituting \(-3\) into the function:

\[
-3 + k = 7
\]

To solve for \( k \), we rearrange the equation:

\[
k = 7 + 3
\]
\[
k = 10
\]

Thus, the value of \( k \) is \( \boxed{10} \).

This means the function that describes the translation is \( g(y) = y + 10 \).