Observe the quantities, ie. see what happens if you increase one or decrease the other.
To simplify imagination, expose one quantity. I will expose y.
1.
[tex]-\frac{y}{4}=2x\implies y=-8x[/tex]
So what is their variation or proportion? If I increase x then y is getting more and more negative. So is this direct or inverse or nothing? It is direct.
2.
[tex]14x=\frac{14}{y}\implies y=x, y\neq0[/tex] again if I increase x then y will match, will also increase. This is again direct.
3.
[tex]y=\frac{13}{x}, x\neq0[/tex] this time if I increase x, y will get smaller. When x is exactly 13, y will be 1 and when x is 10000, y will be 0.0013. This is inverse. One quantity gets really small when other quantity gets really big.
4.
[tex]y=x-2[/tex] if I increase x then y will also increase even though by slightly less (-2) it will still increase. However since there is no multiplication this is not a direct variation nor is it inverse. It is nothing/no-variation.
Hope this helps :)
