Question

Graph each inequality by hand.

$2x+y\ge 6$

Short answer

The required graph is

Step-by-step solution

Step 1. Given Information 

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

Step 2. Plotting the graph 

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

The graph of the inequality$2x+y\ge 6$is a solid line and so is part of the graph of the inequality. Since $\left(0,0\right)$does not satisfy the inequality, the graph consists of the plane away from the origin. The shaded portion represents the inequality. The graph is