Answer:
y' = 1/2 x - 1
Explanation:
Definition of Translation
A translation is a transformation that moves a geometric figure a certain distance in a certain direction. The figure is moved as a whole, without changing its size or shape. The direction of the translation is specified by a vector, and the distance of the translation is the magnitude of the vector.
Equation of a Translated Line
The equation of a translated line can be found by adding the translation vector to the equation of the original line. For example, if a line is translated by a vector (h, k), then its equation changes as follows:
Original equation: y = mx + b
Translated equation: y = mx + b + k
In this case:
The equation of the line is y = ½ x + 1. If this line is translated -2 units on the y-axis, then the translation vector is (0, -2).
The equation of the translated line is therefore:
y = ½ x + 1 - 2
y = ½ x - 1
Therefore, the equation that represents the image of the line y = ½ x + 1 after a translation of -2 units on the y-axis is y' = ½ x - 1.