DIRECT AND INVERSE VARIATION

Direct Variation:
Word: Two quantities x and y exhibit direct variation if when one quantity x increases(decreases) ,  other quantity y increases(decreases) by the same factor of k so that the quotient of x and y is unchanged. K is the constant of variation. 

Algebraic: x and y exhibit direct variation if they satisfy the following equations
\(y = kx\) (Function Form) or  \(\frac{y}{x} = k\)  (Relation Form) or   \(\frac{{{y_1}}}{{{x_1}}} = \frac{{{y_2}}}{{{x_2}}}\)  (Proportion Form)  or  \(y \propto x\)  (Variation Form)

Graphical:
Graphically a direct variation can be represented using a straight line that goes through the origin. The slope of the line as illustrated below is the k value the constant of variation. 

INVERSE VARIATION

Inverse Variation:
Word: Two quantities x and y exhibit inverse variation if when one quantity x increases(decreases) , the other quantity y decreases(increases) by the same factor of k so that the product of x and y is unchanged. K is the constant of variation. 

Algebraic: x and y exhibit direct variation if they satisfy the following equations\(y = \frac{k}{x}\)  (Function form) or \(yx = k\) (Relation Form)  or    
\({y_1}{x_1} = {y_2}{x_2}\)  (Proportion Form)  or   \(y \propto \frac{1}{x}\)  (Variation Form)

Graphical:
Graphically an inverse variation can be represented using the graph of a rational function.