## Part III - Affine Equations in 2D and 3D

#### Affine Equation

A nonhomogeneous linear equation or system of nonhomogeneous linear systems of equations is said to be affine.

Example: Ax+By+C is an affine function of two variables.
Consider the function Ax+By+C in 2-dimension, and set C=0 to start,

Draw the level lines Ax+By = constant

**If B=0,**

Ax = constant

So x = constant/A

**If B0,**

y = (const - Ax)/B

They are non-vertical lines.

We want a uniform way to describe the level lines of Ax+By without separating into cases B=0 and B0.

Ax+By=0

[A,B] * [x,y] = 0

[A,B][x,y]

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