Question

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.?

Answer 1

If `(x,y)` represents a direct variation 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.