A student tries to determine whether or not the data pairs (1, 24) (2, 12) (3, 8) and (4, 6) show direct variation. Describe and correct the error in the students work:

1*24 = 24 2*12 = 24
3*8 = 24 4*6 = 24
Because the products xy are constant, y varies directly with x.

Question

A student tries to determine whether or not the data pairs (1, 24) (2, 12) (3, 8) and (4, 6) show direct variation. Describe and correct the error in the students work:

1*24 = 24             2*12 = 24
3*8 = 24               4*6 = 24
Because the products xy are constant, y varies directly with x.

anonymous · Answer

When two variable quantities have a constant (unchanged) ratio,
their relationship is called a direct variation. 
It is said that one variable "varies directly" as the other.  
1:24                      2:12
3:8                         4:6

anonymous · Answer

Yes but why is the student's work incorrect @xHamstersx

anonymous · Answer

The student didn't show the ratio between y and x.

anonymous · Answer

So in order to correct the mistake I would have to show the ratio but how would I show that?

anonymous · Answer

the ratio = y/x ... in this case, the pairs have different ratios so its not a direct variation.

anonymous · Answer

Okay thank you @xHamstersx

anonymous · Answer

No problem :D