Question

Suppose y varies directly as x, and y = 27 when x = 3. Find y when x = 4.

Answer 1

y = 36

Explanation:

given y varies directly as x then the equation relating them is

y = kx ← k is the constant of variation

to find k use the condition y = 27 when x = 3 , then

27 = 3k ( divide both sides by 3 )

9 = k

y = 9x ← equation of variation

when x = 4 , then

y = 9 × 4 = 36

Answer 2

the initial statement is y ∝ x

to convert to an equation multiply by k the constant of variation

`y = kx`

to find k use the given condition

`y = 27 \\ \\ when \\ \\ x = 3`

`y = kx \\ \\ k = (y)/(x) = (27)/(3) = 9`

equation is y = 9x

when x = 4 then

`y = 9 * 4 = 36.`