Question

What is the direct variation equation for the table of ordered pairs?

x y
20 24
30 36
40 48

Answer 1

Hi.

x = 10
y = 12

I got the answer because the the first row down is just the 10 times table. 10, 20, 30, 40. The second row down is the 12 times table. 12, 24, 36, 48.

Hope this helped!
Have a great day :)

Answer 2

The direct variation says that:

`y \propto x`

then the equation is in the form of : y =kx.....[1] where k is the constant of variation.

From the table:

Consider any values of x and y.

Let x = 20 and y =24

Substitute these values in [1] to solve for k;

`24 = 20k`

Divide both sides by 20 we get;

`1.2 = k`

⇒
`y = 1.2x`

Check:

Substitute any values of x and y.

x= 30 and y =36

`y = 1.2x`

36 = 1.2(30)

36 = 36 True.

Therefore, the direct variation equation for the table of ordered pairs is,
`y = 1.2x`