For each equation, determine whether it represents a direct variation, an inverse variation, or neither. find the constant of variation when one exists and write it in simplest form.

we know that in direct variation as x increase y also increases.

in indirect variation x decreases y increase and vice versa.

in part a we have x at top (numerator ) and y at denominator it mean indirect variation (as x increases y decreases).

to find k we know that for indirect variation xy=k

if we rewrite the equation x=9/y we get xy=9

which mean k=9 .

in part b we have 4xy=20 if we simplify this equation we get

so here if we rewrite in terms of x.

we get x=5/y which represents indirect variation.

and we know xy=k

we have xy=5 .so k=5