# What is the equation of the line perpendicular to #y=-5/8x # that passes through # (-6,3) #?

##### 2 Answers

#### Explanation:

Consider the standard equation form of a strait line graph:

A straight line that is perpendicular to this will have the gradient:

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Given equation:

The equation perpendicular to this will be

'~~~~~~~~~~~~~~~~~~~~~~~~~~

We know it passes through the point

Substitute this point into equation (2) giving:

So equation (2) becomes:

I opted for fractional form for consistency of format. This is because the 5 in

If

Here

Therefore slope of the given line is

If two lines are perpendicular then the product of their slopes is

Let the slope of the line perpendicular to the given line be

Then by definition

This is the slope of required line and the line required line also passes through

Using point slope form

This is the required line.