step 1
Find out the equation of the line
we have the points
(9,6) and (-3,-2)
Find out the slope
m=(-2-6)/(-3-9)
m=-8/-12
m=2/3
The equation is of the form
y=mx+b
we have
m=2/3
point (9,6)
substitute and solve for b
6=(2/3)(9)+b
6=6+b
b=0
therefore
y=(2/3)x -----> the given line represents a direct variation
so
Verify each ordered pair
Find out the value of K (constant of proportionality K=y/x)
(12,8) ------> k=8/12=2/3 ----> the point lie on the same line
(-18,-12)------> k=-12/-18=2/3 -----> the point lie on the same line
(6,0) ------> k=0/6=0 ---> not lie on the same line
(-6,-4) ----------> k=-4/-6=2/3 -------> the point lie on the same line
(3,2) -------> k=2/3 -------> the point lie on the same line
(4,6) -----> k=6/4=3/2 ----> not lie on the same line