Chapter 1, Problem 133RE

To determine

To calculate:The equation that depicts $M$ varies directly with respect to $z$ and also, $M=120$ and $z=15$

Answer to Problem 133RE

The required equation is $M=8z$

Explanation of Solution

Given information:

Here $M$ varies directly with respect to $z$ and also, $M=120$ and $z=15$

Formula used:

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

  $x\alpha y$

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:

  $x\alpha \frac{1}{y}$

Which can be written as:

  $x=k\left(\frac{1}{y}\right)$

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 $M$ varies directly with respect to $z$ .

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

  $x\alpha y$

Which can be written as:

  $x=ky$

Where $k$ denotes the proportionality constant.

Hence, this variation can be expressed as follows:

  $\begin{array}{l}M\alpha z\\ M=kz\end{array}$ $\left(1\right)$

Where $k$ denotes the proportionality constant.

It is also given $M=120$ and $z=15$

Put these values in $\left(1\right)$ to get:

  $\begin{array}{l}120=k\left(15\right)\\ k=\frac{120}{15}\\ k=8\end{array}$

Replace the value of $k$ in $\left(1\right)$ to get the required equation as:

  $M=8z$

Thus, the required equation is $M=8z$