Direct Proportionality

It is said that y is directly proportional to x if their ratio is constant, i.e. `y/x=k` or `y=kx`.

Direct proportionality is a function of the form `y=kx`, where `k!=0`. Number k is called coefficient of proportionality.

Properties of the function y=kx:

  1. Domain of the function is all number line (set R of real numbers).
  2. Function is odd, because `f(-x)=k(-x)=-kx=-f(x)`.
  3. When k>0, function is increasing, when k<0, function is decreasing on all number line.

Fact. Graph of the function `y=kx` is line, that passes through the origin.

direct proportionality

On the figure to the right you can see graphs of function y=kx when k>0 and k<0.

Example. Draw graph of the function y=2x.

graph of the function y=2xTo draw graph of the function y=2x, we need to find only one point (except origin, i.e. (0;0)) and draw line through the origin and found point. So, if x=1 then `y=2*1=2`. Therefore, we can take point `(1,2)`.