Chapter 9.4, Problem 13IP

a.

To determine

To determine the direct variation is true or false for a given graph.

Answer to Problem 13IP

The direct variation for a given graph is True.

Explanation of Solution

Given information

On the given graph, there are three given points $\left(0,3\right),\left(2,4\right)$ and $(6,6)$ .

  

Calculation:

The direct variation is true or false for a given graph.

For Determine Direct Variation.

Taking any two points from the given graph.

  $(0,3)$ and $(2,4)$

  $\begin{array}{l}\text{slope}\text{of}\text{line}=\frac{\text{change}\text{in}y}{\text{change}\text{in}x}\\ m=\frac{4-3}{2-0}\\ m=0.5\end{array}$

Since, the value of m is positive.

Therefore,

There is direct variation exist.

b.

To determine

To determine for the given graph is linear relationship exists or not.

Answer to Problem 13IP

True

Explanation of Solution

Given:

The given line graph.

  

Calculation:

Since,

The graph is straight line and has slope $0.5$ at all points. It has a linear relationship.