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Graphing Overview

Ok, here's the glitch:

Let's try to graph this:

2x - 3y = 0

Well, it's form 1: Ax + By = C ...

Let's go for the intercepts...

an x y table showing one 0 at the top of the x column and one 0 at the bottom of the y column ignore the 2x part of the equation 2x - 3y = 0, which gives y = 0 an x y table showing one 0 at the top of the the x column and one 0 at the top of the y column
an x y table showing one 0 at the top of the x column and two 0's in the y column ignore the -3y part of the equation 2x - 3y = 0, which gives x = 0 an x y table showing two 0's in the x column and two 0's in the y column

Not very helpful, was it?

We have ONE point on our graph:

a graph of the point ( 0, 0 )

2x - 3y = 0 ... The 0 is the problem, so what do we do?

Let's change it to form 2! y = mx + b

Check it out:

                                        2x - 3y = 0 ... get the y alone by subtracting 2x from both sides, which gives -3y = -2x ...divide both sides by -3, which gives y = -2x / -3, which gives y = ( 2 / 3 )x

 

Well, it almost looks like y = mx + b ...

How about this?

y = ( 2 / 3 )x + 0

Now, THIS I can graph!

start at ( 0 , 0 ) on a graph ...which we already had then "rise" 2 and "run" over 3 ... to the point ( 3 , 2 ) ...the resulting graph is a straight line with the slope 2 / 3

YOUR TURN:

Graph x + 4y = 0