Solve for y

2y+2x=4

Question

Solve for y

2y+2x=4

anonymous · Answer

Looking for an explanation of how to solve for y, not just the answer. (Divide everything by 4? by 2? Help please) Thanks!

anonymous · Answer

y=2-x

johnweldon1993 · Answer

Well we start with

$$\large 2y + 2x = 4$$

the first thing we want to do...is move everything that ISN'T 'y' to the other side of the equation...so here....we have a 2x on the same side as the 2y....so lets subtract 2x from both sides of this equation

$$\large 2y + 2x \color \red{- 2x} = 4 \color \red{- 2x}$$

now we have
$$\large 2y = 4 - 2x$$

Alright...now we want to solve for 'y'....we have 2y...so we divide EVERYTHING by 2....

$$\large \frac{2y}{2} = \frac{4 - 2x}{2}$$
which will become
$$\large y = 2 - x$$

but we will always want to write this with the 'x' in front of the constant...so lets write it as

$$\large y = -x + 2$$

anonymous · Answer

Thank you ^

johnweldon1993 · Answer

No problem :)

anonymous · Answer

One more question, if you are still available @johnweldon1993 . 

This is a linear equation that I am suppose to graph. How do I get the slope? (y=mx+b) 
I assume it's just 1 or -1, but I could be confused.

johnweldon1993 · Answer

No you got it...

the form $$\large y = mx + b$$ is slope intercept form....'m' is the slope...and since our equation is $$\large y = -x + 2$$  our 'm' would be -1

anonymous · Answer

And since slope is always written as a fraction (rise/run), would it be written as -1/1 ?

johnweldon1993 · Answer

Well...yes...but as you can see $$\large \frac{-1}{1} = -1$$ It Is good to write it like that if you are not comfortable with seeing just -1 as a slope...but either way is correct

anonymous · Answer

Oh, duh. Thank you for your help, I appreciate it.

johnweldon1993 · Answer

anytime :)