Question

The values of (x) and (y) vary directly, and one pair of values is given: (x=2), (y=5) (in tion form). Write the equation that relates the values of (x) and (y), and simplify completely.

a) (y = 5/2x)
b) (y = 2x)
c) (y = x/5)
d) (y = 5x)

Answer 1

Main Answer:

The main answer (y = 2x) reflects the direct variation between (x) and (y), with a constant of proportionality of 2. (b)
`\(y = 2x\).`

Therefore, the correct answer is b) (y = 2x).

Step-by-step explanation:

In a direct variation, the relationship between two variables, like (x) and (y), is expressed in the form
`\(y = kx\), where \(k\)` is the constant of proportionality. Given the pair of values (x=2) and (y=5), we can substitute these values into the equation and solve for
`\(k\):`

`\[5 = k * 2\]`

Solving for
`\(k\),` we find that
`\(k = 2\)`. Substituting \(k\) back into the general equation, we get
`\(y = 2x\).` This indicates that the values of (x) and (y) vary directly, with
`\(y\)` being twice the value of
`\(x\).` Therefore, option (b)
`\(y = 2x\)` is the correct equation.

This equation aligns with the given values, where if
`\(x = 2\),` then
`\(y = 2 * 2 = 4\),` matching the provided (x=2, y=5) pair.

In summary, the correct equation is
`\(y = 2x\)` as it accurately represents the direct variation between (x) and (y) with the given pair of values.

Therefore, the correct answer is b) (y = 2x).