Question

If y varies directly as x, and y is 48 when x is 6, which expression can be used to find the value of y when x is 2?

Answer 1

Direct variation is of the form y=kx, where k is the constant of variation. We are given the point (6,48) so we can solve for k:

48=6k divide both sides by 6

8=k, so the equation is:

y=8x, then when x=2

y=8(2)

y=16

Answer 2

An expression can be used to find the value of y when x is 2 is,

y=8x ; Value of y = 16 when x = 2

Explanation:

Direct variation states:

If y varies directly as x

⇒
`y \propto x`

then the equation is in the form of:

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

As per the statement:

If y varies directly as x, and y is 48 when x is 6.

⇒
`y = kx`

y = 48 when x = 6

Substitute the given values in [1] and solve for k we have;

`48= 6k`

Divide both sides by 6 we have;

8 = k

or

k = 8

Then, an equation we have;

y =8x ....[2]

We have to find value of y when x is 2.

Substitute the value of x = 2 in [2] we have;

`y = 8(2) = 16`

Therefore, an expression can be used to find the value of y when x is 2 is,

y=8x and Value of y = 16 when x = 2