Question

Determine whether y varies directly with x. If so, find the constant of variation k and write the equation.

Answer 1

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.

Answer 2

Answer:

Option: A is the correct answer.

  A) Yes; k = 4; y = 4x

Step-by-step explanation:

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:

               $y=kx$

Hence, we get:

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

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.

$k=\dfrac{24}{6}=4$

$k=\dfrac{72}{18}=4$

$k=\dfrac{216}{54}=4$

$k=\dfrac{648}{162}=4$

Since, the ratio is same in each of the case.

Hence, we get:

Constant of proportionality= 4

and the equation is:   y= 4x