Chapter 8.3, Problem 14WE

To determine

To graph: The equation of line $y-3x-2$ .

Answer to Problem 14WE

The slope of the line is: $m=3$ .

Explanation of Solution

Given information:

The equation of the line, $y-3x-2$ .

Graph:

The graph of the line $y-3x-2$ can be sketched using the traces,

Rewrite the equation $y-3x-2$ ,

As the equation becomes:

  $\begin{array}{l}y-3x-2\\ y=3x+2\end{array}$

Now plot the equation on the graph:

  

From the graph take two points:

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

  $\begin{array}{c}y=3x+2\\ y=3\cdot 0+2\\ y=2\end{array}$

which are intersecting lines in xy plane.

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

  $\begin{array}{c}y=3x+2\\ 0=3x+2\\ -2=3x\\ \frac{-2}{3}=x\\ x=-0.667\end{array}$

Now the points on the line are:

If

  $\begin{array}{l}x=0,then:y=2\\ y=0,then:x=0.667\end{array}$

Interpretation:

The general equations is of a line .

A line has two coordinates.

It is the straight line that crosses the $x$ -axis at $-0.667$ and $y$ -axis at $2$ .

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

  $\begin{array}{l}x=0,y=2\\ y=0,x=-0.667\end{array}$

Therefore,Thepoints on the graph of line is:

  $\begin{array}{l}x=0,y=2\\ y=0,x=-0.667\end{array}$