How do you put equations into Y= Form?

Question

How do I change the following equations into y= form so I can graph them!

1. 3x-2y=6

2. 4x=3y-9

Please explain how you did it, thanks!

Answer 1

1. 3x-2y=6
Move -2y to right side of equation getting:
3x = 2y +6 [When you move a term from one side to the other you must change its sign]
Now move the 6 to the left sid getting:
3x-6 = 2y
Now divide both sides by 2 getting:
3x/2 -3 = y

2. 4x=3y-9
Move -9 to left hand side getting:
4x+9 = 3y
Now divide both sides by 3 getting:
4x/3+3 = y

Don't forget to change sign when you move terms from one side of the equation to the other.

Answer 2

Imagine a plate scale in equilibrium, the equal sign being the center.
As in a real plate scale if you add or remove the same weight in the two plates, equilibrium will stand.
You do the same in the equation: if you add the same 'thing' to the both sides of the equation, the equality stands.

So, let's begin to add (-3x) to the first one:

- 3x + 3x - 2y = 6 - 3x

(- 3x + 3x = 0 )

- 2y = 6 - 3x

Now lets divide by -2:

- 2y/-2 = (6 - 3 x)/-2

y = -1/2 (6 - 3x) = -3 + 3/2x = 3/2 x - 3

(of course you need to know how to do the basics operations.)

4x = 3y - 9

4x + 9 = 3y - 9 + 9 (+9 in the plates)

4/3 x + 3 = y ( * 1/3 or / 3) (9/3 = 3)

y = 4/3 x + 3

Answer 3

Y Form