Line L passes through the points (4 , -5) and (3 , 7). Find the slope of any line perpendicular to line L.

Given the points ( 4, -5) and the point ( 3, 7) passes
through line L.

We need to find the slope of any
perpendicular line to L.

First we will determine the slope
of L.

We know that:

m =
(y2-y1)/(x2-x1) = (7+5) / (3-4) = 12/-1 = -12

Now we know
that the product of the slopes of two perpendicular line is
-1.

==> Let m1 be the slope of any perpendicular
line.

==> m * m1 =
-1

==> -12 * m1 =
-1

==> m1=
1/12

The slope of any perpendicular line to L
is 1/12.