Question

Which set of ordered pairs is not a direct variation?

{(2,6), (8,12), (14,18)}
{(6,6), (12,12), (18,18)}
{(3,6), (6,12), (9,18)}
{(2,6), (4,12), (6,18)}

Answer 1

The first option is not a direct variation

Explanation:

When we talk of a direct variation, as one value increases, the other value increases too

Or as one value decreases, the other value decreases

A direct variation is of the form;

y = kx

k = y/x

where k is the coefficient of variation that must be a constant value all through the set of values

The values we are comparing here are the x and y values

So

let us take a look at the options;

The first option is not a direct variation

For the first option, the rate of increase is not constant;

2/6 = 1/3 , 8/12 = 2/3 , 14/18 = 7/9

for the second;

the ratio is 1 to 1

for the third;

3/6 = 1/2 ; 6/12 = 1/2; 9/18 = 1/2

for the fourth;

2/6 = 1/3, 4/12 = 1/3 , 6/18 = 1/3