Question

If y varies directly with x, and if y = 12 when x = 3, how do you find the direct variation equation?

Answer 1

If
`\(y\)` varies directly with
`\(x\)` and
`\(y = 12\)` when
`\(x = 3\)` , you can find the direct variation equation by using the formula
`\(y = kx\)` , where
`\(k\)` is the constant of variation.

Step-by-step explanation:

In the case of direct variation, the relationship between
`\(y\)` and
`\(x\)` is expressed as
`\(y = kx\),` where
`\(k\)` is a constant. To find the constant of variation
`(\(k\)),` substitute the given values for \(y\) and \(x\) into the equation.

Given that
`\(y = 12\)` when
`\(x = 3\):`

`\[12 = k * 3\]`

Solving for
`\(k\):`

`\[k = (12)/(3) = 4\]`

Now that you know
`\(k = 4\),` you can write the direct variation equation:

`\[y = 4x\]`

So, in this case, the direct variation equation is
`\(y = 4x\).`

In summary, to find the direct variation equation, substitute the given values into the
`\(y = kx\)` formula and solve for the constant of variation
`(\(k\)).`