Question

The variables x and y are proportional. Use the values to find the constant of proportionality. Then write an equation that relates x and y. Write any fractions in the simplest form. When y=20 , x=12.

Answer 1

Given:

y is proportional to x.

y=20 and x=12.

To find:

The constant of proportionality and the equation for the proportional relationship.

Solution:

y is proportional to x.

`y\propto x`

`y=kx` ...(i)

Where, k is the constant of proportionality.

Putting y=20 and x=12, we get

`20=k(12)`

`(20)/(12)=k`

`(5)/(3)=k`

Putting
`k=(5)/(3)` in (i), we get

`y=(5)/(3)x`

Therefore, the contestant of proportionality is
`k=(5)/(3)` and the equation for the proportional relationship is
`y=(5)/(3)x`.