Proportional Relationships

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yalialp06

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When we graph a proportional relationship where the context is telling us that there can't be any negative values for x and y, is it correct to have an end point at the origin and not continue the line down and to the left. For example, if x is the hours I work, and y is the money I earn, I cant work negative hours or make negative money so extending the graph down and to the left doesn't make sense so why do we represent these types of functions like this?
My second question is... if in a proportional relationship the constant of proportionality is found by calculating y/x then how can the origin be explained? How can it be explained that the constant of proportionality can not be found by using the point (0,0).
 
Yes, if x and y can't be negative then you should not have the graph contain any points where x or y is negative.

If y/x = k, where k is some constant, then y = kx. You decide why this line passes through the origin. If you can't figure it outthink please post back asking for help.
 
I know the line passes through the origin bc if i work zero hours, then I'll make zero money, but lets suppose a point on that line is (1,10) and y/x=k. Then k=10 and is the constant of proportionality, but when i look at the origin and calculate y/x=k, the value of k is not 10. How can k=0/0 be explained? I'm probably just thinking too much into it.
 
The equation of the line is y=10x.
The equation of the line can be expressed as y/x = 10, except when x=0. The graph of y/x=10 is actually a straight line with a little hole in it where (0, 0) should be.
 
yalialp06 said:
I know the line passes through the origin bc if i work zero hours, then I'll make zero money, but lets suppose a point on that line is (1,10) and y/x=k. Then k=10 and is the constant of proportionality, but when i look at the origin and calculate y/x=k, the value of k is not 10. How can k=0/0 be explained? I'm probably just thinking too much into it.
Click to expand...

Here is an answer I gave to the question about zero a few years ago, that deals with your issues and a couple others:

 
I think this is very helpful. What was most helpful was when you said that proportionality is the relationship between two variables, not two numbers. Thank you!
 
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