# What is the equation of the line perpendicular to #y=6x # that passes through # (6,-1) #?

##### 2 Answers

Different way of saying the same thing:

#### Explanation:

Given:

Compare to the standard equation form of

Where

Looking at the question we see that the gradient is 6.

This means that for 1 along on the x-axis the line has gone up 6 on the y-axis.

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If

So the straight line perpendicular to that given has the equation

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This line passes through the point

So by substitution

so the equation of the perpendicular line is:

#### Explanation:

When lines are perpendicular, one slope is the negative reciprocal of the other.

In

The slope perpendicular to this is

We now have the slope and the point

There is really nifty formula which applies in a case like this. We have the slope and one point and need to find the equation of the line.

Substitute the values given.