Question

If y varies directly as x, and y is 18 when x is 5, which expression can be used to find the value of y when x is 11?

a.y=5/18(11)
b.y=18/5(11)
c.y=(18)(5)/11
d.y=11/(18)(5)

Answer 1

B. 18/5(11), because when solving for k using the equation y=kx than you get 18/5 and then multiply by 11.

Answer 2

Option b is correct

`y=(18)/(5)(11)`

Explanation:

The direct variation says that:

`y \propto x`, then the equation is of the form:

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

As per the statement:

If y varies directly as x.

By direct variation:

`y = kx` ....[1]

If y = 18 when x = 5

Substitute these values in [1] we have;

`18 = 5k`

Divide both sides by 5 we have;

`(18)/(5)= k`

or

`k = (18)/(5)`

⇒
`y = (18)/(5)x` ......[2]

We have to find the value of y when x = 11.

Substitute x = 11 in [2] we have;

`y = (18)/(5) \cdot 11 = (18)/(5)(11)`

Therefore, the value of y is,
`(18)/(5)(11)`