Chapter 9.3, Problem 23IP

Solution

a.

To calculate: Slope of the line represented by the data in the table.

Slope of the line is $-2$ .

Given information:

The following table:

Formula used:

Slope is given by the formula,

  $m=\frac{y_2-y_1}{x_2-x}$

where $x_2\ne x$ .

Calculation:

Take any two points from the table such as $(-1,-6)$ and $(0,-8)$ .

Slope is calculated as follows:

  $\begin{array}{l}m=\frac{y_2-y_1}{x_2-x}[\text{Definition of slope]}\\ m=\frac{-8-(-6)}{0-(-1)}[(x_1,y_1)=(-1,-6),(x_2,y_2)=(0,-8)]\\ m=\frac{-2}{1}[\text{Simplify]}\\ m=-2[\text{Divide]}\end{array}$

b.

To graph: The given data in the table and connect the points with a line.

Given information:

The following table:

Graph:

Graph of the given data is obtained as follows:

c.

To explain: Representation by the point $(0,-8)$ .

The point $(0,-8)$ represents the point of intersection of the line and the y -axis.

Given information:

The following table:

Explanation:

The graph of the data given in the table is obtained as follows:

The point $(0,-8)$ represents the point of intersection of the line and the y -axis.