I am in Introductory Algebra and I am unsure on how to graph a linear equation. Can someone please help me. The equation is -7x-y=2

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- shadowfiend

Can you graph an equation written in the form y = mx + b?

- anonymous

From what I was reading in my book that is the formula that helps give the answer but I dont know if my answer is right.

- shadowfiend

Well it's currently tough to graph on OpenStudy, but the first thing to do with the above equation is to get it in that form, y = mx + b. Have you already done that/do you know how?

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- anonymous

That is where I am having the problem. I don't know how to do that correctly.

- shadowfiend

Ok. So the key here is that we want y to be alone, and we want it to be positive. I generally like to start by making y positive.
Can you move the y in -7x - 7 = 2 to the right side of the equation?

- shadowfiend

-7x - y = 2, sorry.

- anonymous

I know that it has to be positive and I think if I add 7x to both sides it might help but again I am unsure about that answer

- shadowfiend

That's actually one way to go about it. So let's try that:
-7x - y = 2
-7x + 7x - y = 2 + 7x
The -7x + 7x cancels out, so we have:
-y = 2 + 7x
We can reorder the right side so we have:
-y = 7x + 2
Now, our model is y = mx + b, so there's just one thing still wrong: the - on the left side. Do you have an idea for how to get rid of it?

- anonymous

I do believe that you would have to divide by -1 on both sides

- shadowfiend

Right -- dividing or multiplying would do the same thing. So you have:
(-1)(-y) = (-1)(7x + 2)
y = (-1)(7x) + (-1)(2)
y = -7x + (-2)
y = -7x - 2

- shadowfiend

So now we have y = mx + b, where m = -7 and b = -2.

- anonymous

and those are the points that I would graph correct?

- shadowfiend

Not quite. They tell you what the graph will look like.
In particular, -7 is the slope, which indicates rise over run. So that means if your graph starts at (0, 0), it will `rise' -7 (or drop 7) on the y axis for every 1 x value.
-2 is the y-intercept, which means that when x is 0, y will be -2.
So you have the starting point: (0, -2), and you have the slope, which tells you that at x = 1, y = -9, which means the second point is (1, -9). And then you can draw a line between the two.
Make sense?

- anonymous

Thank you so much that really helps me out. It makes a lot of sense now that I can understand it.

- shadowfiend

Awesome! Good to hear!

- anonymous

finding the slope of a line would be taking two points of the graph and using y=mx+b?

- anonymous

You would use the slope formula. Assuming you have two points (x1,y1) and (x2,y2).
The slope m = (y2-y1)/(x2-x1).

- anonymous

actually the equation is x=3

- shadowfiend

The slope in the case of x = 3 is what we call `undefined'. Basically, rise over run gives us a number divided by zero (actually infinity divided by zero), because x = 3 means a line going straight up and down at x = 3.

- anonymous

Thank you I did not know that. My instructor did not explain that too well.

- shadowfiend

No problem!

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