Question

Determine the constant of variation for the direct variation given.R varies directly with S. When S is 16, R is 80.

Answer 1

"R varies directly with S" means R=?S.
R=5S
Constant of variation for the direct variation would be 5.

Answer 2

The direct variation says that:

`y \propto x` then;

the equation is of the form:

y = kx , where k is the constant of variation.

As per the given statement:

R varies directly with S.

By definition of direct variation:

`R = kS`

Substitute the given values S = 16 and R = 80 to solve for k;

`80 = 16k`

Divide both sides by 16 we get;

5 = k

⇒R=5S

Therefore, the constant of variation is, 5