Question

Find the variation constant and an equation of variation for the given situation.

y varies directly as x, and y = 7 when x = 1/2.

Answer 1

`\displaystyle y=14\cdot x`

Explanation:

Directly Proportion

It's said that y varies directly proportional as x, if:

`y=k\cdot x`

Where k is a constant of proportionality.

We know that y=7 when x=1/2.

Using the above condition, we can find the value of k:

`\displaystyle 7=k\cdot (1)/(2)`

Solving for k:

k=14

Thus, the equation is:

`\boxed{\displaystyle y=14\cdot x}`