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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)

User Igelgrun
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1 Answer

4 votes

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).

User CristiC
by
8.4k points

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