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Parallel lines have the same slope. Can you determine the slope of the given line?

I do not know how to find the slope of these two.

3y = 5x?

How do I simplify it?

Combine like terms on the left hand side. The right hand side can't be simplified any further.

Is it 2 + 3y = 6 - x ?

What is \(x - x\) ?

0? or just x?

y = -x + 3 ?

The left hand side is OK. But you didn't divide the -x by 3 and 6/3 is not 3. Can you fix it up?

y = -x + 2

I was confused of that turning into a decimal I see now.

Ok. So you got the slope y+a=-1/3(x+a)

The two a are different sorry about that.

Is it supposed to be written as y = -1/3x +2 ?
Or no y into it?

Well, there are 2 ways to write it. I find my way uses less calculations

Is the -1 I get from -1/3(3)
supposed to be b?

* \(+ b\) sorry for the typo

I made a typo. It should read\[4 = -\frac{ 1 }{ 3 }\left( 3 \right) + b\]sorry bout that

Its no problem ! I do not get how to solve for b.

OK. What do you get when you multiply -1/3 x 3 ?

I get -1 for that.

Do I add +1 to b as well?

No. It looks like this:\[4+1 = -1 + b + 1\]Now simplfy

Is it 5 = b ?

Yayyyy! Good work.

y = -1/3x +5?

Perfect. Well done. That is the line that is parallel to \(x+3y=6\) that passes through \((3, 4)\)

You're doing a good job. With some additional practice maybe math could be your best subject :)

That is true indeed. Also again thank you !

You're welcome