Question

A line is represented by y = 4x + 3. A perpendicular line goes through (8,5). What would be the slope intercept form for the perpendicular

line?

Answer 1

y =
`-(1)/(4)`x + 7

Explanation:

Given expression:

y = 4x + 3

Coordinate = (8,5)

Unknown:

The equation of a line perpendicular = ?

Solution:

A line perpendicular will have slope that is the negative inverse of the one given.

Equation of a straight line;

y = mx + c

y and x are the coordinates

m is the slope

c is the y- intercept

For y = 4x + 3;

slope is 4;

A perpendicular line will have a slope of
`-(1)/(4)`

Let us find the y-intercept of the new line;

y = 5, x = 8

5 =
`-(1)/(4)` x 8 + c

5 = -2 + c

c = 7

the equation of the line perpendicular is;

y =
`-(1)/(4)`x + 7