# How do you write an equation in slope-intercept form for a line with (4, -1) and perpendicular to a line with equation 3x + y = 4?

##### 1 Answer

#### Explanation:

A linear equation in the form

The given line

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

If two lines are perpendicular the slope of one is the negative reciprocal of the other.

Any line perpendicular to

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

A line with a slope of

can be written in slope-point form as:

A line perpendicular to

can be written as:

which would typically be simplified as

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

Here is a graph with these two equations and the required point for verification:

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

**Note 1**

If you are not familiar with slope of

it can be easily derived by converting to slope intercept form:

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

**Note 2**

For some the more common general slope-point form might be

I prefer the form that I have used above since it avoids the exclusion problem when