Let's see how two points on the left are mapped to their corresponding points on the right:
Point A has a corresponding point at A'. We have:
f(A) = A'
f(-6, -3) = (2, 4)
Point B has a corresponding point at B'. We have:
f(B) = B'
f(-4, -1) = (4, 6)
Now, notice that:
2 = -6 + 8
4 = -3 + 7
So, for (x, y) = (-6, -3), we have:
f(x, y) = (2, 4) = (x + 8, y + 7)
Notice that the same happens to the mapping of the other point:
4 = -4 + 8
6 = -1 + 7
So, for (x, y) = (-4, -1), we have:
f(x, y) = (4, 6) = (x + 8, y + 7)
Therefore, the rule for the transformation is
f(x, y) = (x + 8, y + 7)