Chapter 1.10, Problem 75E

To determine

To find:if the given statement is true or false.

Answer to Problem 75E

True

Explanation of Solution

Given:

The statement: “If y is directly proportional to x and x is directly proportional to z , then y is directly proportional to z ”.

Concept Used:

For the variables pand q , the statement pis directly proportionalq can be translated as:

  $p=kq$

Where k is a non-zero constant called the constant of proportionality.

Now, the given statement is “ y is directly proportional to x .”

So, by the definition in above step and using $k_1$ as the constant of proportionality, given statement can be translated as:

  $y=k_{1}x$ ….. (1)

Also, the given statement is “ x is directly proportional to z .”

So, by the definition in above step and using $k_2$ as the constant of proportionality, given statement can be translated as:

  $x=k_{2}z$ ….. (2)

From (1) and (2),

  $\begin{array}{c}y=k_{1}x\\ =k_1\left(k_{2}z\right)\\ =\left(k_1{k}_2\right)z\end{array}$

Since $k_1{k}_2$ is also a constant. So, by definition of directly proportional it can be said that y is directly proportional to z .