|Jan27-13, 07:19 AM||#1|
Proportionality and graphs
Quote from Wikipedia:
|Jan27-13, 07:48 AM||#2|
In math, two quantities are proportional, by definition, if their ratio is constant.
i.e. if y is proportional to x, then y/x=k - a constant.
The graph would be y=kx - which is a special case of a straight line.
If you translated the graph, changing the reference point for measuring x for instance, then the equation of the line is:
y=k(x+a) and the graph of x vs y no longer passes through the origin.
The quantities x and y are no longer proportional (y/x=k+ka/x - not a constant) because it is a different x - instead it is x+a that is proportional to y ... which is fair, because x+a was the original quantity.
However, we can still say that
y1 = k(x1+a)
y2 = k(x2+a)
y2-y1 = k(x2-x1)
so changes in y are proportional to changes in x.
If two quantities x and y are related by some line y=mx+c, then the relationship is just called "linear".
|Jan27-13, 07:54 AM||#3|
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