Firstly, let's understand that the slope of a line is a measure of the vertical change (rise) for each unit of horizontal change (run). The formula for calculating the slope of a line connecting two points `A(x1, y1)` and `B(x2, y2)` is given by `(y2 - y1) / (x2 - x1)`.
Using this formula, we can find the slope of the line between the points A(-3,2) and C(-1,6). Subtract the `y` coordinates of point A from point C to calculate the 'rise' (i.e. 6 - 2 = 4 ). Then, subtract the `x` coordinates of point A from point C to calculate the 'run' (i.e. -1 - (-3) = 2). By dividing the rise by the run, we find that the slope of line AC is 2.
Next, recall that the slope of a line perpendicular to a given line is the negative reciprocal of the original line's slope. By finding the negative reciprocal of the slope of line AC (which is 2), we obtain -1/2. This means that the slope of the line passing through point B and perpendicular to line AC is -0.5.
In conclusion, the slope of line AC is 2 and the slope of the line through point B that is perpendicular to line AC is -0.5.