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Write y as a function of x

Given the equation: 2x - 3y = 6

Write y as a function of x.


I know this is straightforward, and I have the line-by-line answer, but I can't understand how you get from:

(2x - 3y = 6)
- 3y = - 2x + 6 (So here you have shifted the 2x over as you want ultimately just y on the left)
to
y = 2x/3 - 2 (Where's the -3? Why is there a fraction on the right? What's happened to the +6?)

:s-smilie:
Reply 1
Avatar for sussexy
sussexy
You divided both sides by -3.

−3y−3=y\frac{-3y}{-3} = y

−2x−3=2x3\frac{-2x}{-3} = \frac{2x}{3}

6−3=−63=−2.\frac{6}{-3} = -\frac{6}{3} = -2.
Reply 2
Avatar for tymbnuip
tymbnuip
OP
1
Oh so you do it to the +6 AND the -2x. Got ya! :smile:
Reply 3
Avatar for tymbnuip
tymbnuip
OP
1
How would I then find the "intercept" and the "root"?
Reply 4
Avatar for sussexy
sussexy
The root is basically the value of x for which y = 0. So set y to and solve for x.

The y-intercept is the value of y for which x = 0. So set x to 0 and solve for y.
Reply 5
Avatar for SamTheMan
SamTheMan
17
tymbnuip
Oh so you do it to the +6 AND the -2x. Got ya! :smile:


Yes you're "doing it" to the sides of the equation rather than the actual terms (at least that's one way of looking at it).

If you didn't, your equation would not hold. There's only a limited number of valid operations you can do to an equation (an equation states that something on the left side is equal to something on the right side) like add/subtract a number to each side or multiply the left expression and the right expression by the same factor (in your case that factor is -3)
Reply 6
Avatar for tymbnuip
tymbnuip
OP
1
The root (x -intercept) is when y = 0

2x/3 - 2 = 0

2x - 6 = 0 {multiply both sides by 3}

So how does the /3 disappear by multiplying by 3? Wouldn't it turn into 9?
Reply 7
Avatar for sussexy
sussexy
tymbnuip
So how does the /3 disappear by multiplying by 3? Wouldn't it turn into 9?


2x3−2=0\frac{2x}{3} - 2 = 0

2x3.31−2.31=0.31\frac{2x}{3} . \frac{3}{1} - 2 . \frac{3}{1} = 0 . \frac{3}{1}

2x−6=02x - 6 = 0

When multiplying two fractions, multiply the top by the top and the bottom by the bottom

2x times 3 = 6x

3 times 1 = 3

6x/3 = 2x

Get it?
Reply 8
Avatar for tymbnuip
tymbnuip
OP
1
What does the =0.3/1 mean?
Reply 9
Avatar for sussexy
sussexy
Urgh sorry

it means 0 times 31\frac{3}{1}
Reply 10
Avatar for tymbnuip
tymbnuip
OP
1
Heh okay. :smile: So I guess now I have 2x - 6 = 0 I want to get rid of the 6?

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