If two variables show a direct variation, it means that y increases/decreases each time x increases/decreases, this means that, if x increases, so do y, and if x decreases, y decreases as well.
You can express it as:
[tex]y=kx[/tex]Where "k" represents the constant fo variation
If two variables have an inverse relationship, as x increases, y decreases, and vice versa.
You can express this relationship as follows:
[tex]y=\frac{k}{x}[/tex]For table "a" the values of y decrease as the values of x increase, to determine if they vary proportionally, you have to determine the value of k for each ordered pair:
To determine the constant of proportionally you have to multiply both coordinates:
[tex]k=xy[/tex]1) (-3,16)
[tex]k_1=(-3)\cdot16=-48[/tex]2) (4,-12)
[tex]k_2=4\cdot(-12)=-48[/tex]3) (6,-8)
[tex]\begin{gathered} k_3=6\cdot(-8) \\ k_3=-48 \end{gathered}[/tex]The constant of proportionality is equal for all sets of values, so you can say the relationship is proportionally inverse following the equation:
[tex]y=-\frac{48}{x}[/tex]For table "b", If you compare the first two sets of values, it seems that y decreases as x increases. But If you compare the second and third ordered pairs, x increases and y is constant.
Since y does not vary for x=4 and x=6, then you can conclude that the relationship does not show a direct or indirect relationship.
