Chapter 8.3, Problem 20WE

To determine

To graph: The equation of line $x-3y=9$ .

Answer to Problem 20WE

The slope of the line is: $m=\frac{1}{3}$ .

Explanation of Solution

Given information:

The equation of the line, $x-3y=9$ .

Graph:

The graph of the line $x-3y=9$ can be sketched using the traces,

Now plot these points on the graph:

  

From the graph take two points:

For $x=0$ , the trace of the surfaces is,

  $\begin{array}{c}x-3y=9\\ 0-3y=9\\ -3y=9\\ y=-\frac{9}{3}\\ y=-3\end{array}$

which are intersecting lines in xy plane.

For $y=0$ , the trace of the surfaces is,

  $\begin{array}{c}x-3y=9\\ x-3\cdot 0=9\\ x=9\end{array}$

Now the points on the line are:

If

  $\begin{array}{l}x=0,then:y=-3\\ y=0,then:x=9\end{array}$

Interpretation:

The general equations is of a line .

A line has two coordinates.

In this graph a line is formed, that shows two points that are:

  $\begin{array}{l}x=0,y=-3\\ y=0,x=9\end{array}$

It is the straight line that crosses the $x$ -axis at $9$ and $y$ -axis at $-3$ .

Therefore,Thepoints on the graph of line is:

  $\begin{array}{l}x=0,y=-3\\ y=0,x=9\end{array}$