Answer:
Step-by-step explanation:
The constant of proportionality is usually presented as the variable k. It is usually written as:
f(x) = kx
where f(x) means a function of x. It can also be another variable, for example, y,
We test each pair to find k,
24 = 6k
k = 24/6 = 4
72 = 18k
k = 72/18 = 4
216 = 54k
k = 4
648 = 162k
k = 4
Thus, the answer is A. yes and k=4.
Option: A is the correct answer.
A) Yes; k = 4; y = 4x
We know that if two variables x and y varies directly by a constant of proportionality k then the equation which describes this relation is given by:
[tex]y=kx[/tex]
Hence, we get:
[tex]k=\dfrac{y}{x}[/tex]
Here we have the table of values as:
x y
6 24
18 72
54 216
162 648
Now, we will check each of the ratio of y and x and see whether they are equal in each case, if they will be then the variables are in direct variation.
[tex]k=\dfrac{24}{6}=4[/tex]
[tex]k=\dfrac{72}{18}=4[/tex]
[tex]k=\dfrac{216}{54}=4[/tex]
[tex]k=\dfrac{648}{162}=4[/tex]
Since, the ratio is same in each of the case.
Hence, we get:
Constant of proportionality= 4
and the equation is: y= 4x
