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

Answer:

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