Answer
Yes, this ration represents a direct variation.
Equation: y=-1.5x
Work Step by Step
In order for a table to represent a direct variation, the ratio of $\frac{y}{x}$ needs to be constant so lets divide each y value with its respective x value.
9/-6=-1.5
-1.5/1=-1.5
-12/8=-1.5
Since the ration is constant, this table represents a direct variation. Now, in order to write the equation, plug in our constant k which we found by dividing y by x, into the standard form of a direct variation (y=kx)
y=-1.5x
