Question

The line contains the point (3,2) and is perpendicular to the line with a lope of -3/4. Enter answer in point-slope form.

Answer 1

The form of point-slope of the linear equation is

`y-y_1=m(x-x_1)`

Where:

m is the slope of the line

x1 , y1 are the coordinates of a point on the line

Perpendicular lines have additive multiplicative inverse slopes which means the product of their slopes is -1

If the slope of one is m, then the slope of the other is - 1/m

We change its sign and reverse its value

m * -1/m = -1

Since the slope of the line is -3/4

Then the slope of the line perpendicular to it is 4/3

We changed the sign and reciprocal the fraction

Therefor m = 4/3

The line passes through the point (3, 2)

Then x1 = 3 and y1 = 2

Let us substitute m, x1, y1 in the form of the equation above

`y-2=(4)/(3)(x-3)`

This is the form of the equation