Which statement describes the function through the points?

The function is linear but not a direct variation function.

Step-by-step explanation:

A function is said to be of direct variation if:

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)

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

As the slope is constant.

   Hence, the function is linear.

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

(10,18)

(14,24)

(18,30)

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

            Hence, the points are not in direct variation.

a.) list the factors of 40.

1/2/4/5/8/10/20/40

b.) list the factors of 40 that represent the number of cans that could be on each shelf.

5

c.) how many different arrangements of cans are possible?

just one because if you put more on one shelf you will go way over 40 and the cabinet will probably break.

d.) what are the possible arrangements of the cans?

put 5 cans on each self to reach 40 cans in total.

e.) which arrangement uses all the shelves?

5 because you can put 5 cans on each shelf, and since there are 8 shelfs you are equally going to get 40 cans.