Problem:
3y = 4x + 1

Question: Tell whether equation represents a direct variation. If so, identify the constant of variation (k).

I'm trying the help the next door neighbor and it's been too long since I've dealt with algebra. Please help me. How is this solved and what is the answer to the question?

It is saying that y is directly proportional to x.

Then, it is asking sort of "by how much does x vary as y varies?"

To do that you have to have your equation in the form y = mx + c where m is the answer you're looking for which gives a constant variation of the function (if I may say so) and c another constant.

Tell your neighbour to try making y alone.

It is saying that y is directly proportional to x.

Then, it is asking sort of "by how much does x vary as y varies?"

To do that you have to have your equation in the form y = mx + c where m is the answer you're looking for which gives a constant variation of the function (if I may say so) and c another constant.

Tell your neighbour to try making y alone.

Sorry, that just confused me more.

Ok... hmm, in any type of linear equation, y = mx + c,

m is the gradient and c is a constant.

m is a constant of variation, so you need to find that m.

But to do this, you have to make y alone, not 2y, nor 5y, etc.

In your problem, you have 3y. What do you do to make is become y?

Ok... hmm, in any type of linear equation, y = mx + c,

m is the gradient and c is a constant.

m is a constant of variation, so you need to find that m.

But to do this, you have to make y alone, not 2y, nor 5y, etc.

In your problem, you have 3y. What do you do to make is become y?

I don't know if English is your second language but your question is confusing "What do you do to make is become y?"
I don't mean that in a disrespectful way but I asked for help on this and you haven't answered the question I originally asked. Throwing the m and c in there just confused me more so I know the 9th grader next door isn't going to have a clue. If you could actually answer the question and maybe walk me through how to solve it, I would greatly appreciate it. If I were to try and solve for y, I would divide both sides by 3. That doesn't answer the equation either because x is still on the other side of the equation. Do you know the answer to the question that I asked originally? If not, I still appreciate the effort.

Sorry, typo from mine, that should have been "What do you do to make 3y become y?"

You have to find the 'm' that I told you.

So, you have 3y = 4x + 1

How to make 3y become y? It's by dividing both sides by 3, like this:

\frac{3y}{3} = \frac{4x + 1}{3}

That becomes:

y = \frac{4}{3}x+\frac{1}{3}

Your 'm' as I told you is 4/3.

Note that we are not supposed to directly give answers as per the announcements that you can see in board in red.

Sorry, typo from mine, that should have been "What do you do to make 3y become y?"

You have to find the 'm' that I told you.

So, you have 3y = 4x + 1

How to make 3y become y? It's by dividing both sides by 3, like this:

\frac{3y}{3} = \frac{4x + 1}{3}

That becomes:

y = \frac{4}{3}x+\frac{1}{3}

Your 'm' as I told you is 4/3.

Note that we are not supposed to directly give answers as per the announcements that you can see in board in red.

well crap. I didn't see that about the direct answers. I was working it right... still stuck though. Thanks for trying to help. Appreciate it.

But hey, don't give up!

Yes the equation is a direct variation. I think I have to get from the start...

If y is proportional to x;

y \propto x

It means that is has a direct relationship with respect to x. Now, when we remove the proportionality sign, we get a constant, k, that we usually call 'm'.

y \propto x

y = kx + c

Lastly, you may have a constant, just like in integration, here, we'll call is 'c'.

No, coming back to the problem, you want to find the 'k'.

3y = 4x + 1

Here, k is NOT 4 because y has got a value in front of it. So we need to remove that 3, and this is done by dividing everything by 3. Then you continue as I said above.

If the equation was : y = 5x - 1
Your constant of variation would be 5

If that was : 2y = x + 5
You change it first to : y = 0.5x + 2.5
Then, the constant of variation becomes 0.5, or 1/2.

Did you get it?

He said in the first post that m was the constant of variation. It has to be in the given format in order to know what the m is. He's given 2 examples in that format, showing what m is.

You have to isolate the y on one side, which essentially means solving for y, but yes the x is still going to be on the one side. In your one post you divided by 3 but said that the problem was the x was still on the other side, which I guess is what is confusing you. But it's supposed to be there. You don't need to get rid of x to know what m is. You only need to get it into the proper format to get m. Which you seem to have. And post #6 outright has the answer to.

So what exactly are you stuck on? No one can explain more to you unless you say what you aren't understanding. (It appears you're not familiar with the y=mx + c format. If not, then that's what you need to ask.)