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:
[tex]\dfrac{y}{x}=k[/tex]
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)
[tex]=\dfrac{24-18}{14-10}=\dfrac{3}{2}[/tex]
Slope of (14,24) and (18,30)
[tex]=\dfrac{30-24}{18-14}=\dfrac{3}{2}[/tex]
As the slope is constant.
Hence, the function is linear.
Now we will check whether it is of direct variation or not.
(10,18)
[tex]=\dfrac{18}{10}=\dfrac{9}{5}[/tex]
(14,24)
[tex]=\dfrac{24}{14}=\dfrac{12}{7}[/tex]
(18,30)
[tex]=\dfrac{30}{18}=\dfrac{5}{3}[/tex]
As the ratio of the y-value to x-value is not constant.
Hence, the points are not in direct variation.
