# How do you find a standard form equation for the line that is perpendicular to #6x-2y+5=0# and has the same y-intercept as #x-y+8=0#?

##### 2 Answers

When given an equation of a line of the form:

The family of perpendicular lines are of the form:

Where k is an unknown constant.

#### Explanation:

Given:

The family of perpendicular lines are:

We must find the y intercept of the line

Substitute the point

Substitute this into equation [1]:

Equation [2] is the answer.

This is the same as:

#### Explanation:

First consider

This can be written as:

So the y-intercept for this equation is 8.

Thus the equation we are looking for passes through the point:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Consider the given equation:

Add

Divide both sides by 2

Thus the gradient (slope) for

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Compare

where

A line that is perpendicular to it will have the gradient of:

Thus our standardised form for the new line is:

From

So

Thus

So the equation of the perpendicular line is: