Question

Discuss the equation $2x-3y=12$. Graph it.

Short answer

The graph of the equation is

Step-by-step solution

Step 1. Given Information

The equation of the is $2x-3y=12$. We need to plot the graph of the equation.

Step 2. Finding the slope and intecept

The standard form of the equation of a line is $y=mx+c$where $m$is the slope of the line and $c$is the intercept on the $y$-axis.

Comparing the equation with the standard form we get:

$$\begin{gathered} \therefore 2x-3y=12 \\ \Rightarrow 3y=2x-12 \\ \Rightarrow y=\frac{2}{3}x-4 \end{gathered}$$

$\therefore m=\frac{2}{3},c=-4$

Step 3. Plotting the graph

The graph of the line is: