# What is the equation of the line that passes through #(6,-4)# and is perpendicular to the line that passes through the following points: #(-2,12),(5,-6) #?

##### 1 Answer

See a solution process below:

#### Explanation:

First, we need to determine the slope of the line passing through

Where

Substituting the values from the points in the problem gives:

Let's call the slope of a perpendicular line:

Then the rule for find the slope of a perpendicular line is:

Substituting gives:

We can now use the point slope formula to find an equation of the line for the point given in the problem and the slope we calculated. The point-slope form of a linear equation is:

Where

Substituting again gives:

Or