Question

Use a table of values to graph each equation.

$4x-3y=12$

Short answer

The table of values to graph the given equation $4x-3y=12$is:

$x$	$y=\frac{4}{3}x-4$	$\left(x,y\right)$
60	$y=\frac{4}{3}\left(0\right)-4=-4$	$\left(0,-4\right)$
$-3$	$y=\frac{4}{3}\left(-3\right)-4=-8$	$\left(-3,-8\right)$
$-6$	$y=\frac{4}{3}\left(-6\right)-4=-12$	$\left(-6,-12\right)$
3	$y=\frac{4}{3}\left(3\right)-4=0$	$\left(3,0\right)$
$6$	$y=\frac{4}{3}\left(6\right)-4=4$	$\left(6,4\right)$

The graph of the given equation $4x-3y=12$is:

Step-by-step solution

Step1. Given 

$4x-3y=12$

Step2. Write a table of values to graph the given equation 4x−3y=12.

It can be noticed that:

$$\begin{gathered} 4x-3y=12 \\ 4x-12=3y \\ \frac{4x-12}{3}=y \\ \frac{4}{3}x-4=y \end{gathered}$$

The table of values to graph the given equation $4x-3y=12$is:

$x$	$y=\frac{4}{3}x-4$	$\left(x,y\right)$
0	$y=\frac{4}{3}\left(0\right)-4=-4$	$\left(0,-4\right)$
$-3$	$y=\frac{4}{3}\left(-3\right)-4=-8$	$\left(-3,-8\right)$
$-6$	$y=\frac{4}{3}\left(-6\right)-4=-12$	$\left(-6,-12\right)$
3	$y=\frac{4}{3}\left(3\right)-4=0$	$\left(3,0\right)$
6	$y=\frac{4}{3}\left(6\right)-4=4$	$\left(6,4\right)$

Step3. Draw the graph of the given equation 4x−3y=12.

The graph of the given equation $4x-3y=12$is: