Know if a constant is on a line.

[phrox]

I just need some help with a basic question I can't remember from a long time ago, just started up school again....

How can I know if there is a constant c on the line x + by = 0 if it has a slope of -4? Explain this please.

 

[Ackbach]

It's not quite clear what the phrase "constant on a line" is. Do you mean is there a point of a certain kind on a line? Can you post the original question word-for-word?

 

[phrox]

It's not quite clear what the phrase "constant on a line" is. Do you mean is there a point of a certain kind on a line? Can you post the original question word-for-word?

http://i1301.photobucket.com/albums/ag115/phrox1/mathprob_zpsfc7c910e.png

I'm also not sure of that. This is the whole question

 

[Ackbach]

Ok, it all makes sense now, although I am not a fan of the problem's wording. It should read like this:

Determine whether there exists a constant $c$ such that the line $x+cy=0$ has slope $-8$.

The "Has slope $-8$" is not a new sentence.

So, how do you think you could proceed on this problem? What is the slope of a line of the form $x+cy=0$?

 

[phrox]

Well I guess the slope right now is 1, but I'm not sure because I guess that 0 just looks weird in there to me which is throwing me off. Where does the -8 go in the equation? Before the x? If so, the answer is supposed to just be a number and there will be x and y values in the end, isn't that right?

 

[Ackbach]

Well, we need to be careful. When it comes to lines, I use only the slope-intercept form: $y=mx+b$. I don't worry about the standard form, the point-slope form, the two-point form, or anything but the slope-intercept form. Can you convert the equation you're given into slope-intercept form? I think if you do that, it might suggest the solution of the problem.

 

[phrox]

1/8 Thanks!

 

[Ackbach]

1/8 Thanks!

You got it! And you're very welcome.