When you studied how straight lines define a relationships between an output dependent variable and in independent input variable. The slope of the relationship was a ratio that tells how the output changes when the input changes by 1-unit. The change is a ratio.

Ratios can be defined as direct ratio, a inverse ratio (reciprocal) , or a joint ratio. Symbolically k represents the ratio. The three types of variations are then written as:

1) a direct variation it is expressed as y=kx.

2) an inverse variation has it’s form specified as y=k/x

3) a direct joint variation depends on two variables, call them x and y. This variation can be expressed as z=kxy where z is the output value and x and y are input variables. K remains the proportionality constant.

You can further define variations by using combinations of the basic three variations above. For example:

1) Direct variation that varies with the cubed of the input is written as y=kx^3.

2) Joint relationship that varies with the square of x and inversely with y is written as z=kx^2/y.