# How do you find the slope of a line that is a) parallel to the line given and b)perpendicular to the line with the given equation #2x-5y = -7#?

##### 1 Answer

If a line is expressed by the equation

Starting with the equation given, first add

Add

Divide both sides by

In other words

Comparing with

Any line parallel to this line will have the same slope:

Any line perpendicular to a line of slope

There are several ways to see this.

For example, consider the following steps:

(1) Reflect the original line in the line

(2) Reflect the line in the

The total effect of (1) followed by (2) is a rotation of

Starting with your original line this will result in a line with equation