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)
To find the value of k, we can substitute the y-coordinate of the original point (4,-1) into the function g(y) and set it equal to the y-coordinate of the translated point (4,2).
g(y) = y + k
g(-1) = -1 + k
Since the original point (4,-1) translates to the point (4,2), we know that g(-1) = 2.
Therefore, we have:
2 = -1 + k
To solve for k, we subtract -1 from both sides of the equation:
2 + 1 = k
k = 3
So, the value of k is 3.
To find the value of k in the function g(y) = y + k that describes the translation from (4, -1) to (4, 2), we need to find the difference in the y-coordinates.
The difference in the y-coordinates is:
2 - (-1) = 3
Since the translation moves the point upward by 3 units, the value of k is 3.
Therefore, the value of k is 3.
To find the value of k, we need to determine the vertical distance by which the point is translated. In this case, the point is translated from (4, -1) to (4, 2).
The y-coordinates of the two points are -1 and 2, respectively. To find the vertical distance, we subtract the initial y-coordinate from the final y-coordinate:
Vertical distance = 2 - (-1) = 2 + 1 = 3
Since the function g(y) = y + k describes the translation, we can say that k represents the vertical distance. Therefore, the value of k is 3.