I presume point B is (1, 6)?

The midpoint of the line segment between points A and B is:

((-3 + 1)/2, (2 + 6)/2) = (-1, 4)

The slope of the line segement between points A and B is:

(2 - 6)/(-3 - 1) = -4/-4 = 1

So half of this slope is 1/2. We need the equation for the line that has a slope of 1/2 and passes through the point (-1, 4).

y = (1/2)x + b

where b is the y-intercept.

To find b, just plug in a point on the line. The only point we know is (-1, 4), so...

4 = (1/2)*(-1) + b

4 = -1/2 + b

b = 4 + 1/2 = 9/2

Thus the line is:

y = (1/2)x + (9/2)

-Dan