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:
- Domain of the function is all number line (set R of real numbers).
- Function is odd, because `f(-x)=k(-x)=-kx=-f(x)`.
- 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)`.