Direct variation is characterized by the equation y = kx, where k is some constant term (usually positive, btw, though apparently not in this case).
Inverse variation is modeled by the equation y = k/x, again where k is a constant, usually positive.
When k is positive, direct variation is characterized by a relationship in which when we increase x, y will increase also. Inverse variation means when we increase x, y will decrease.
Ordering the points from smallest to biggest x will help here: (-10 , .8) , (-2 , .16) , (50 , -4). We can see that as the magnitude (absolute value) of x increases, the magnitude of y also increases, therefore we can say these points model direct variation. And because x and y have opposite signs, k will be a negative number:
y = kx let's plug in any one of the points to solve for the constant k
.8 = - 10k
k = - .08 = - 2/25
We can check this value by plugging the other 2 given pts into y = - .08x to confirm they satisfy the equation.
