Q. 11 - Precalculus Enhanced with Graphing Utilities

Question

Graph the equation:

$3x-2y=12$

Step-by-Step Solution

Answer

The graph of the given equation is:

Step 1. Given Information

The given equation is $3x-2y=12$

Step 2. Make a table for values

Writing the equation in terms of $y$, we get:

$$\begin{gathered} 3x - 2y = 12 \\ 2y=3x-12 \\ y=\frac{3}{2}x-6 \end{gathered}$$

Table of values for $x$ and $y$ is:

$x$	$y=\frac{3}{2}x-6$
$0$	$$\begin{gathered} y=\frac{3}{2}\times 0-6 \\ y=-6 \end{gathered}$$
$1$	$$\begin{gathered} y=\frac{3}{2}\times 1-6 \\ y=\frac{3}{2}-6 \\ y=\frac{-9}{2} \end{gathered}$$
$2$	$$\begin{gathered} y=\frac{3}{2}\times 2-6 \\ y=3-6 \\ y=-3 \end{gathered}$$
$3$	$$\begin{gathered} y=\frac{3}{2}\times 3-6 \\ y=\frac{9}{2}-6 \\ y=\frac{-3}{2} \end{gathered}$$

Step 3. Graph the function

Plotting these points on the same cartesian plane and joining them to find them, we get: