If y is 6 when x is 3 and y varies directly with x, find y when x is 8. a) 4 b) 11 c) 16

Question:

If y is 6 when x is 3 and y varies directly with x, find y when x is 8.

a) 4

b) 11

c) 16

Direct Proportion

Two quantities are in direct proportion if on increasing one, the is also increases or on a decrease, the other is also decreases.

For example, Time and Work are directly proportional to each other.

Let's assume that 'A' is proportional to 'B', it means if 'A' increases 'B' is also increases.

{eq}\displaystyle A \propto B {/eq}

{eq}\displaystyle A = kB {/eq}

Here 'k' is the proportional constant.

Given:

'y' varies directly with 'x'

So we can write:

{eq}\displaystyle y \propto x {/eq}

{eq}\displaystyle y = kx {/eq}

Here 'k' is the proportional constant.

Now if y is 6 when x is 3.

So

{eq}\displaystyle 6 = 3\times k {/eq}

{eq}\displaystyle k =\frac{6}{3} = 2 {/eq}

And now if x = 8 then y:

{eq}\displaystyle y = kx = 2\times 8 = 16 {/eq}

So the at x=8 the value of 'y' is 16.

Option C is correct.