Question

Graph each inequality by hand.

$3x+2y\le 6$

Short answer

The required graph is

Step-by-step solution

Step 1. Given Information  

We are given the inequality $3x+2y\le 6$and we need to graph it.

Step 2. Plotting the graph  

First, we plot the equation of the line $3x+2y=6$.

The graph of the inequality$3x+2y\le 6$is a solid line and so is part of the graph of the inequality. Since $\left(0,0\right)$does satisfies the inequality, the graph consists of the plane towards the origin. The shaded portion represents the inequality. The graph is