Question

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

Answer 1

The first set of plots do not line up.

Answer 2

Answer:

The  sets of ordered pairs is NOT a direct variation

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

Step-by-step explanation:

We know that the set of ordered pair are in  direct variation if they lie on a straight line or we can say if the rate of change is constant.

1)

- (0,0) (-2,4) (3, -6)

From the following set of points we see that we get a straight line as:

y= -2x

Hence , the points are in direct variation.

2)

- (1, 1) (-2, -2) (3,3)

Now, these set of ordered points also satisfy the line as:

y=x

Hence, the points are in direct variation.

3)

- (10, 2) (15,3) (20,4)

Now, these set of ordered points also satisfy the line as:

y=(1/5)x

Hence, the points are in direct variation.

4)

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

We find the rate of change of (0,0) and (1,3) as:

$\dfrac{3-0}{1-0}=3$

The rate of change of (1,3) and (2,4) is:

$\dfrac{4-3}{2-1}=1$

As the rate of change is not constant.

Hence, the points are not in direct variation.

Hence,  sets of ordered pairs is NOT a direct variation is:

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