Chapter 9.4, Problem 6IP

To determine

To determine if the relationship between the two quantities is a direct variation.

Answer to Problem 6IP

The relationship between the two quantities is inverse variation.

Explanation of Solution

Given:

Two points on the graph are $\left(20,50\right)$ and $\left(40,30\right)$

  

Concept Used:

Slope of a line is given by $m=\frac{y_2-y_1}{x_2-x_1}$

If the slope of the line is positive, then it is direct variation.

If the slope of the line is negative, then it is inverse variation.

Calculation:

The relationship between the two quantities is a direct variation.

Here the values are,

  $\begin{array}{l}{x}_1=20,x_2=40,\\ y_1=50,y_2=30\end{array}$

The relationship between the two quantities can be obtained as,

  $\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}\\ m=\frac{30-50}{40-20}\\ m=\frac{-20}{20}\\ m=-1\end{array}$

Since, the value of m is negative.

Therefore,

The relationship between the two quantities is not a direct variation.