# How do you determine if the lines through the given points (4,6), (5,3) are parallel and which, if any, are perpendicular?

Nov 16, 2016

#### Explanation:

In general, a line is parallel to another line, if the two lines have the same slope:

$n = m$

A line will be perpendicular to another line if the slope, n of the perpendicular line has the following relationship to the slope, m:

$n = - \frac{1}{m}$

The slope of a line between the two points is:

$m = \frac{3 - 6}{5 - 4} = - 3$

If a line is parallel to the line between these two points, its slope will be $- 3$.

If the line is perpendicular, its slope is $\frac{1}{3}$