Question

suppose that three variables x,y, and x are related by the rule z= kxy with k>0. Considering x>0 andy>0 how will the value of z change if : x is held constant and t increases? x is held constant and t decreases?

Answer 1

Given that the three variables x,y, and z are related by the rule z= kxy with k>0.

This means that x and y are directly proportional to z.

Given that x > 0 and y > 0

For values that are directly proportional, an increase in the independent variable leads to an increase in the dependent variable and a decrease in the independent variable leads to a decrease in the dependent variable.

Therefore, the value of z will increase if x is held constant and y increases.

And the value of z will decrease if x is held constant and y decreases.