If y varies directly as x, and y is 20 when xis 4, what is the constant of variation for this relation?

The constant of variation for this relation is k = 5

Step-by-step explanation:

Step:1

given 'y' varies directly as x that is  

  where k is constant ........(1)

Given y value is 20 and x value is 4

now substitute x = 4 and y=20 in equation (1)

we get solution, 20 = k (4)

dividing '4' on both sides, we get

k = 5

verification:-

y = k x

put k= 5 , y=20 and x= 4

20 = 20

or

step-by-step explanation:

we need to solve for 'x' the following equation:  

we have that:

⇒

⇒ ⇒

factorizing, we get that:

  ⇒

then, the solutions are: or

nothing extraneous has been found!