Question

Graph each inequality by hand.

$x^2+y^2\le 9$

Short answer

The required graph is

Step-by-step solution

Step 1. Given Information 

We are given the inequality $x^2+y^2\le 9$and we need to graph it.

Step 2. Plotting the graph  

First, we plot the equation of the circle $x^2+y^2=9$with center $\left(0,0\right)$and radius $3$.

The graph of the inequality $x^2+y^2\le 9$is a solid circle and so is part of the graph of the inequality. Since $\left(0,0\right)$satisfies the inequality, the graph consists of the portion towards the origin. The shaded portion represents the inequality. All the points on and inside the circle satisfy the inequality. The graph is