When one quantity varies with respect to two or more quantities, we have a combined variation. When one quantity varies directly with two or more quantities, we have a joint variation.
Value of z When x=6 and y =0.5: 8
Practice makes perfect
When one quantity varies with respect to two or more quantities, we have a combined variation. When one quantity varies directly with two or more quantities, we have what is called a joint variation.
Combined Variation
Equation Form
z varies jointly with x and y.
z=k x y
z varies jointly with x and y, and inversely with w.
z=k x y/w
z varies directly with x and inversely with the product w y.
z=k x/w y
Writing the Function That Models the Variation
In our exercise, we are told that z varies directly with x and inversely with y.
z=k x/y
Here k is the constant of variation and it cannot equal 0. To find k we will substitute x= 9, y= 4, and z= 1.5 in the above equation.
