Chapter 9.4, Problem 5IP

To determine

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

Answer to Problem 5IP

The relationship between the two quantities is direct variation.

Explanation of Solution

Given:

Two points on the graph are $\left(2,10\right)$ and $\left(4,20\right)$

  

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.

Slope of the two quantities,

Here the values are,

  $\begin{array}{l}{x}_1=2,x_2=4\\ y_1=10,y_2=20\end{array}$

The relationship between the two quantities can be obtained as,

  $\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}\\ m=\frac{20-10}{4-2}\\ m=\frac{10}{2}\\ m=5\end{array}$

Since, the value of m is positive.

Therefore,

The relationship between the two quantities is a direct variation.