1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Proportionality and graphs

  1. Jan 27, 2013 #1
    Quote from Wikipedia:

    I've been told by people that a graph with a straight line on it can be proportional but only if it passes through the origin. I fail to see why that's true. If a translation was applied and it was moved 1 unit to the right then, all of a sudden, x is not proportional to y anymore? That doesn't make sense to me.
  2. jcsd
  3. Jan 27, 2013 #2

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper

    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".
  4. Jan 27, 2013 #3
    So if the graph is translated left or right, I can still say that "changes in y are proportional to changes in x" but I can't say "y is proportional to x" - is that correct?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook