Question

In the following exercises, graph by plotting points.

$3x-2y=6$

Short answer

The graph of the equation is

Step-by-step solution

. Given information

Equation to be plotted is

$3x-2y=6$

it can be rewritten as

$$\begin{gathered} 3x=6+2y \\ 2y=3x-6 \\ y=\frac{3}{2}x-\frac{6}{2} \\ y=\frac{3}{2}x-3 \end{gathered}$$

Step 2. To find three points whose coordinates are solution to the equation    

When $x=0$

localid="1645013987425" $$\begin{gathered} y=\frac{3}{2}\times 0-3 \\ y=0-3 \\ y=-3 \end{gathered}$$

When$x=2$

$$\begin{gathered} y=\frac{3}{2}\times 2-3 \\ y=3-3 \\ y=0 \end{gathered}$$

When $x=-2$

localid="1645013991475" $$\begin{gathered} y=\frac{3}{2}(-2)-3 \\ y=-3-3 \\ y=-6 \end{gathered}$$

Now arrange these points in a table

x	y	(x,y)
0	3	(0,3)
2	0	(2,0)
-2	6	(-2,6)

Step 3. Plot these points in a rectangular coordinate system       

points(0,3), (2,0) and (-2,6) are plotted as

Step 4. Draw the line through three points and extend the line.    

The line is the graph of the equation