# Chapter 4: Lines and Planes

## Lines

Explicit equation:

Implicit equation:

Consider two known points of a triangle and .

We can use these points to determine the slope and plug into the explicit equation:

Here we have replaced the unknown y-intercept with another constant, . We don’t really care what was so we’ll just move on with .

We know that is on the point, so let’s plug in an solve for .

Plug back in to our original equation with

## Planes

A plane is defined by a point and a normal . The plane consists of all points for which is perpendicular to .

Or, using the dot product:

And to get a more commonly seen equation:

where