# Determine whether the equation represents direct, inverse, joint, or combined variation. { ...

## Question:

Determine whether the equation represents direct, inverse, joint, or combined variation. {eq}y=\frac{31x}{wz} {/eq} .

## Variation:

(i) Direct Variatoion:

If x varies directly as y then {eq}x=my {/eq}, where 'm' is a proportionality constant.

(ii) Inverse Variation:

If x varies inversely as y then {eq}x= \dfrac{n}{y} {/eq}, where 'n' is a proportionality constant.

(iii) Joint Variation:

If a variable {eq}c {/eq} varies jointly with respect to both the variables {eq}a {/eq} and {eq}b {/eq}, then it means that:

$$c= kab $$

where, {eq}k {/eq} is a constant of variation.

(iv) Combined Variation:

If a variation consists of two or more above variations, then it is a combined variation.

## Answer and Explanation:

The given equation is:

$$y=\frac{31x}{wz} $$

By the definition of direct variation and inverse variation, {eq}y {/eq} is directly proportional to {eq}x {/eq} and inversely proportional to {eq}wz {/eq}.

**Therefore, the given variation is a combined variation.**

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from High School Algebra II: Tutoring Solution

Chapter 19 / Lesson 10