# 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.

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.

To 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).