Question

Which statement describes the function through the points?

Answer 1

You're right its B that you already selected

Answer 2

The function is linear but not a direct variation function.

Explanation:

A function is said to be of direct variation if:

`(y)/(x)=k`

where k is a fixed constant for each ordered pair (x,y) on the graph.

We are given a three points in a graph as:

(10,18) , (14,24) and (18,30)

The points seems to be in a straight line hence, the function is linear.

Also we can check the slope to check that the function is linear.

Slope of (10,18) and (14,24)

`=(24-18)/(14-10)=(3)/(2)`

Slope of (14,24) and (18,30)

`=(30-24)/(18-14)=(3)/(2)`

As the slope is constant.

Hence, the function is linear.

Now we will check whether it is of direct variation or not.

(10,18)

`=(18)/(10)=(9)/(5)`

(14,24)

`=(24)/(14)=(12)/(7)`

(18,30)

`=(30)/(18)=(5)/(3)`

As the ratio of the y-value to x-value is not constant.

Hence, the points are not in direct variation.