Question

Suppose y varies directly with x.write a direct variation equation that relates x and y .y=7 1/2 when x=3

Answer 1

as y varies directly with x, the following equation can be established.

y = a * x

from the condition given by the question, we can know that

7.5 = a * 3

a = 7.5 / 3 = 2.5

thus, we can infer that the equation is

y = 2.5 * x

Answer 2

`y=2.5x`

Explanation:

We know that y varies directly with:
`y` ∝
`x`.

To convert this proportionality into an equality, we need a constant
`k`.

`y` =
`kx`

We know that
`y = 7.5` when
`x=3` so we can write it as:

`y` =
`kx`

`7.5` =
`k(3)`

`k =2.5`

Now that we know the value of the constant
`k` is equal to
`2.5` , we can write the this relation as:

`y=2.5x`