Which equation describes this relationship? Remember to include k, the constant of variation. z varies directly with w and inversely with x and y Choices: (A)z = kwy/x (B)z = k/wxy (C)z = kw/xy (D)z = ky/wx

Identify Direct Variation: z varies directly with w and inversely with x and y, so the equation should have w in the numerator and x and y in the denominator. Determine Correct Equation Form: The correct form for the equation of variation is z = k(w)/(xy), because z is directly proportional to w and inversely proportional to both x and y. Match with Choices: Looking at the choices, (C)z = kw/xy matches the form we derived.

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Which equation describes this relationship? Remember to include $k$ , the constant of variation. $\newline$ $z$ varies directly with $w$ and inversely with $x$ and $y$ $\newline$ Choices: $\newline$ (A) $z = \frac{kwy}{x}$ $\newline$ (B) $z = \frac{k}{wxy}$ $\newline$ (C) $z = \frac{kw}{xy}$ $\newline$ (D) $z = \frac{ky}{wx}$

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Algebra 2

Write joint and combined variation equations II

Full solution

Q. Which equation describes this relationship? Remember to include

k

, the constant of variation.

\newline

z

varies directly with

w

and inversely with

x

and

y

\newline

Choices:

\newline

(A)

z = \frac{kwy}{x}

\newline

(B)

z = \frac{k}{wxy}

\newline

(C)

z = \frac{kw}{xy}

\newline

(D)

z = \frac{ky}{wx}

Identify Direct Variation: $z$ varies directly with $w$ and inversely with $x$ and $y$ , so the equation should have $w$ in the numerator and $x$ and $y$ in the denominator.
Determine Correct Equation Form: The correct form for the equation of variation is $z = \frac{k(w)}{xy}$ , because $z$ is directly proportional to $w$ and inversely proportional to both $x$ and $y$ .
Match with Choices: Looking at the choices, $(C)z = \frac{k w}{x y}$ matches the form we derived.