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

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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.**

The slope of the line L passing through the points ( 4 , -5) and (3 , 7) is given by :

slope = ( -5 - 7) / (4 - 3)

=> -12 / 1

The slope of a line perpendicular to this would be m such that m*(-12) = -1

=> m = 1/12

**The required slope of the line is 1/12**

The slope of the given line is:

m = [7-(-5)]/(3-4)

m = 12/-1 = -12

The slope of the perpendicular line is m1 and we know that the product of the slopes of 2 perpendicular lines is -1.

m*m1 = -1

-12*m1 = -1

m1 = 1/12

**The slope of the perpendicular line is: m1 = 1/12.**