A point is translated on the coordinate plane from (4, - 1) to (4, 2). Journey

Question

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 $\boxed{{\displaystyle 3}}$.