Question

Suppose that y varies directly as x, and that y = 12 when x = 3. When x = 10, y =

Answer 1

Rule: y = kx (y varies directly with x)

Then 12=k(3), and k=4. Then the rule (direct variation) becomes y=4x.

Now let x=10. Then y=4(10) = 40 (answer)

Answer 2

Direct variation states that:

`y \propto x`

then, the equation is in the form of:

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

As per the statement:

y varies directly as x, and that y = 12 when x = 3

By direct variation:

y = kx

Substitute the given values we have;

`12 = 3k`

Divide both sides by 3 we have;

4 = k

or

k = 4

⇒ y =4x .....[1]

Now, when x = 10 find y;

Substitute value of x in [1] we have;

`y = 4 \cdot 10 = 40`

⇒y = 40

Therefore, the value of y is, 40