Question

As x increases and y stays constant, z as y increases and x stays constant, zas x increases and z stays constant, y

Answer 1

Consider $z=\frac{x}{y}$

(1) As x increases and y stays constant, z ______

(2) As y increases and x stays constant, z _____

(3) As x increases and z stays constant, y ______

Answer:

$z=\frac{x}{y}$

(1) As x increases and y stays constant, z increases

When y stays constant, z is directly proportional to x. So , as x increases the z also increases.

(2 ) As y increases and x stays constant, z decreases.

When x stays constant, z is inversely proportional to y. So , as y increases the z decreases.

(3) As x increases and z stays constant, y increases

$z=\frac{x}{y}$ (z stays constant)

So equation becomes $y=\frac{x}{z}$

When z stays constant, y is directly proportional to x. So , as x increases the y also increases.