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?(1 point)

Question

Responses

10
10

0
0

-10
-10

4

Answer 1

To determine the value of \( k \) in the function \( g(y) = y + k \) that describes the translation from the point \( (5, -3) \) to the point \( (5, 7) \), we can consider how the \( y \)-coordinate changes.

The original \( y \)-coordinate is \( -3 \), and it is translated to \( 7 \). We can express this translation mathematically:

1. The change in the \( y \)-coordinate is:
   \[ 7 - (-3) = 7 + 3 = 10 \]

2. Thus, we need to add \( 10 \) to the original \( y \)-coordinate of \( -3 \) to reach \( 7 \). This means we have: \[ g(y) = y + 10 \]

From this, it follows that \( k = 10 \).

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