# Given that the slope of a line is -1/5, what is the slope of a line that is perpendicular to it?

##### 3 Answers

#### Answer:

Slope is 5

#### Explanation:

The perpendicular to a given slope is its negative reciprocal. This means the fraction is flipped and multiplied by

#### Answer:

#### Explanation:

The perpendicular slope of any original slope is derived by negating the original slope and then "flipping" the fraction. By "flipping" the fraction, I mean find the inverse of the original slope. So for example:

Original slope:

Step 1. Negate the original slope. Remember that a negative of a negative is a positive.

Step 2. "Flip" the fraction, finding it's inverse. Remember that whole numbers can be turned automatically into fractions by placing them over a 1.

More generally, you can always find the perpendicular slope using this formula:

#### Answer:

All you have to do is remember and follow the method in the first bit of the explanation.

The rest is supportive expansion and contains the actual solution.

#### Explanation:

Let the slope (gradient) of the first line be

Then the gradient of the perpendicular line is

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

This s true for any straight or curved line graph.

The only difference is that for a straight line it is a constant value but for a curved line it changes to suit the gradient at each and every point

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

The given slope is

The gradient of the perpendicular is:

.................................................................................

I left the answer in the format of

For every 1 along you go up 5

The teacher will expect you to write the answer gradient as 5 and not