# The equation that depicts z varies inversely with respect to y and also, z = 12 and y = 16

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 1, Problem 134RE
To determine

## To calculate:The equation that depicts z varies inversely with respect to y and also, z=12 and y=16

Expert Solution

The required equation is z=192y

### Explanation of Solution

Given information:

Here, z varies inversely with respect to y and also, z=12 and y=16

Formula used:

For 2 variables say, x and y , the statement x is directly proportional to y can be written as:

xαy

Which can be written as:

x=ky

Where k denotes the proportionality constant.

Similarly the statement x is inversely proportional to y can be interpreted as:

xα1y

Which can be written as:

x=k(1y)

Where k denotes the proportionality constant.

Slope-intercept equation for a given line which has slope as m and y −intercept as b is:

y=mx+b

Calculation:

As z varies directly with respect to y .

Recall, For 2 variables say, x and y , the statement x is inversely proportional to y can be interpreted as:

xα1y

Which can be written as:

x=k(1y)

Where k denotes the proportionality constant.

Hence, this variation can be expressed as follows:

zα1yz=ky (1)

Where k denotes the proportionality constant.

It is also given z=12 and y=16

Put these values in (1) to get:

12=k16k=12*16k=192

Replace the value of k in (1) to get the required equation as:

z=192y

Thus, the required equation is z=192y

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