MHB Know if a constant is on a line.

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To determine if a constant c exists on the line x + cy = 0 with a slope of -4, clarification on the problem's wording is necessary. The discussion reveals that the original question should state whether there exists a constant c such that the line has a slope of -8. Participants emphasize the importance of converting the equation into slope-intercept form to find the slope. The final consensus suggests that understanding the relationship between the coefficients and the slope will lead to the solution. The conversation highlights the need for clarity in mathematical problem statements to facilitate better understanding.
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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.
 
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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?
 
Ackbach said:
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
 
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 $x+cy=0$?
 
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?
 
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.
 
1/8 :) Thanks!
 
phrox said:
1/8 :) Thanks!

You got it! And you're very welcome.
 
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