Mathematics 47 Online
OpenStudy (anonymous):

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

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

OpenStudy (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.

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?

OpenStudy (anonymous):

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

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?

-7x - y = 2, sorry.

OpenStudy (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

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?

OpenStudy (anonymous):

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

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

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

OpenStudy (anonymous):

and those are the points that I would graph correct?

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?

OpenStudy (anonymous):

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

Awesome! Good to hear!

OpenStudy (anonymous):

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

OpenStudy (anonymous):

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

OpenStudy (anonymous):

actually the equation is x=3

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.

OpenStudy (anonymous):

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