The ordered pair (1.5, 6) is a solution of direct variation, how do you write the equation of direct variation? Represents inverse variation. Represents direct variation. Represents neither.?

If ##(x,y)## represents a solution then ##y = m*x## for some constant ##m##

Given the pair ##(1.5,6)## we have ##6 = m*(1.5)## ##rarr m=4## and the direct variation equation is ##y= 4x##

If ##(x,y)## represents an inverse variation solution then ##y = m/x## for some constant ##m##

Given the pair ##(1.5,6)## we have ##6 = m/1.5## ##rarr m = 9## and the inverse variation equation is ##y = 9/x##

Any equation that can not be rewritten as one of the above is neither a direct nor an inverse variation equation. For example ##y=x+2## is neither.