11-18 Class notes - What type of variation. Function equation from a table.

If a problem indicates inverse variation, you are looking for a relationship where y = k/x or xy = k.
X appears in the denominator.  K is divided by x.

If a problem indicates direct variation, you are looking for a relationship where y = kx.
K is multiplied by x.


If, for the (x,y) ordered pairs of a function, y1 / x1  =  y2 / x2  =  y3 / x3  = . . . = the same constant k, then k is the coefficient of direct variation.  The shape of a direct variation graph is a straight line, and y / x is analogous to the slope, change in y divided by change in x.


If, for the (x,y) ordered pairs of a function, x1 times y1 = x2 times y2 = x3 times y3 = . . . = the same constant k, then k is the coefficient of inverse variation.