Question

Which statement describes the function through the points?

Answer 1

You're right its B that you already selected

Answer 2

Answer:

The function is linear but not a direct variation function.

Step-by-step explanation:

A function is said to be of direct variation if:

$\dfrac{y}{x}=k$

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)

$=\dfrac{24-18}{14-10}=\dfrac{3}{2}$

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

$=\dfrac{30-24}{18-14}=\dfrac{3}{2}$

As the slope is constant.

   Hence, the function is linear.

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

(10,18)

$=\dfrac{18}{10}=\dfrac{9}{5}$

(14,24)

$=\dfrac{24}{14}=\dfrac{12}{7}$

(18,30)

$=\dfrac{30}{18}=\dfrac{5}{3}$

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

            Hence, the points are not in direct variation.