The general algebraic expression to represent a translation has the form:
(x+a, y+b)
Where the points are translated "a" points to the right and "b" points up.
From the given figure, we can see that the point "S" goes from (-6, -3) to (-2, 2)
Then, we can formulate the following expressions, to find "a" and "b":
x-coordinate of point S + a = x-coordinate of point S'
-6 + a = -2
-6 + 6 + a = -2 + 6
a = 4
y-coordinate of point S + b = y-coordinate of point S'
-3 + b = 2
-3 + 3 + b = 2 + 3
b = 5
Then, the algebraic expression that represents this translation is:
(x + 4, y + 5)
Then, the correct answer is the last option