Question

The variables x=2 and y=7 varies directly. How do you write an equation that relates the variables and find y when x=8?

Answer 1

`y=28`

Explanation:

“The variables `x=2` and `y=7` vary directly.”

We can express that as:

`y=mx`

`\rightarrow 7=m\cdot 5`, where `m` is the constant of variation (slope).

Now, we need to solve for `m`:

`7=2m`

Divide both sides by `2`:

`m=\frac{7}{2}`

Now, we can plug this value, as well `x=8`, into the next equation to find `y`:

`y=mx`

`\rightarrow y=\frac{7}{2}\cdot 8`

`\rightarrow y=\frac{56}{2}`

`\rightarrow y=28`

Answer 2

`y =7/2x`
`y(8)=28`

Explanation:

I assume you mean that `x and y` vary directly and `x=2` when `y=7`

If so, then we know that:

`y = kx` for some constant `k`

Since `x=2` when `y=7`

`:. 7 = kxx2`

`->k=7/2`

Hence, `y =7/2x` is our required equation.

We are asked to find `y` when `x=8`

`-> y(8)=7/2xx8 = 7xx4`

`y(8)=28`