Question

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

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Answer 1

k = 5

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 = 20 when x = 4, then

20 = 4k ( divide both sides by 4 )

5 = k

Answer 2

The value of k = 5

Explanation:

We know when y varies directly as x, we get the equation

y ∝ x

y = kx

Here 'k' is the 'constant' of proportionality

Given

• y = 20, when x = 4

so substituting y = 20, x = 4 in the equation y = kx

y = kx

20 = k(4)

k = 20 / 4

k = 5

Therefore, the value of k = 5