Question

Suppose Y varies directlly With x. If y= 6 when x=2 find x when y= 12

Answer 1

Answer: x=4

Explanation:

By definition, the direct variation eqution has the following form:

`y=kx`

Where k is the constant.

Therefore, if If
`y=6` when
`x=2`, you can calculate k as following:

-Substitute values.

- Solve for k.

Then:

`6=k(2)\\k=3`

Then, when
`y=12`, you can calculate the value of x as it is shown below:

-Substitute values.

- Solve for x.

Then:

`12=3x\\x=4`

Answer 2

The value of x = 4 when the value of y = 12

Explanation:

∵ y α x ⇒ it is direct variation

- It means y increase when x increase

∴ y = kx ⇒ where k is a constant

- To find the value of k we will substitute the values of x

and y in the equation above

- If y = 6 when x = 2

∴ 6 = k(2) ⇒ divide two sides by 2

∴ k = 3

∴ y = 3x ⇒ equation of variation

- To find the value of x when y = 12

- Substitute the value of y in the equation of variation

∴ 12 = 3x ⇒ divide both sides by 3

∴ x = 4

* The value of x = 4 when the value of y = 12