# How do you find equation of line which is perpendicular to the line #2x-3y=5# and passes through the point (2,1)?

##### 1 Answer

Jan 3, 2017

Swap the coefficients, make one negative, and then use the point to solve for the new constant.

#### Explanation:

When given the equation of a line in the form:

It is very easy to make a line that is perpendicular to the given line:

- Swap a and b
- Change the sign of either a or b
- Make the right side an arbitrary constant, k

The two possible results are shown below:

or

For the given line,

Given the point

Substitute 7 for k into equation [3]:

Equation [4] is the answer.