Chapter 8.3, Problem 17WE

To determine

To graph: The equation of line $3x+2y=6$ .

Answer to Problem 17WE

The slope of the line is: $m=-\frac{3}{2}$ .

Explanation of Solution

Given information:

The equation of the line, $3x+2y=6$ .

Graph:

The graph of the line $3x+2y=6$ 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,

  $\begin{array}{c}3x+2y=6\\ 3\cdot 0+2y=6\\ 2y=6\\ y=\frac{6}{3}\\ y=2\end{array}$

which are intersecting lines in xy plane.

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

  $\begin{array}{c}3x+2y=6\\ 3x+2\cdot 0=6\\ 3x=6\\ x=\frac{6}{3}\\ x=2\end{array}$

Now the points on the line are:

If

  $\begin{array}{l}x=0,then:y=3\\ y=0,then:x=2\end{array}$

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:

  $\begin{array}{l}x=0,y=3\\ y=0,x=2\end{array}$

It is the straight line that crosses the $x$ -axis at $2$ and $y$ -axis at $3$ .

Therefore,Thepoints on the graph of line is:

  $\begin{array}{l}x=0,y=3\\ y=0,x=2\end{array}$