Question

Which of the following sets of ordered pairs is not a direct variation?

(0, 0); (-2, 4); (3, -6)
(1, 1); (-2, -2); (3, 3)
(10, 2); (15, 3); (20, 4)
(0, 0); (1, 3); (2, 4)

Answer 1

The last choice is not direct variation.

Explanation:

Direct variation can be written as y = kx where k is a constant.

The ordered pairs are values of (x, y).

Thus the first set is direct variation and the rule is

y = -2x.

We see by substitution that this is the rule:

0 =-2*0 = 0

4 = -2*-2 = 4.

-6 = -2*3 = -6.

We see that, in each case, y/x = -2.

The last set is not direct variation as

y/x = 3/1 = 3 but 4/2 = 2.

Answer 2

(0, 0); (1, 3); (2, 4)

Explanation:

The above-listed points are not on a line with constant slope, so do not represent direct variation.