Chapter 11, Problem 80RE

To determine

Graph each inequality.

Answer to Problem 80RE

  

Explanation of Solution

Given information:

Graph each inequality.

  $2x-3y\ge 6$

Calculation:

Let us consider inequality

  $2x-3y\ge 6$

First we replace the inequality sign $"\ge "$ with $"="$ and find the equation

  $2x-3y=6$

And then sketch the graph of this equation.

Now we test the point $\left(0,0\right)$ on the given inequality as

  $2\left(0\right)-3\left(0\right)\ge 6$

  $0\ge 6$

Since $0\ge 6$ is a false statement, the point $\left(0,0\right)$ is not a solution of the inequality.

And hence the complete solution is set of all the points which are opposite side of the line as the point $\left(0,0\right)$ , including all the points on the line $2x-3y=6$ itself.

So, the solutions of $2x-3y\ge 6$ are given by the point in the half-plane above the line and the graph is sketched in the rectangular Cartesian coordinate system as given below:

  

Hence, the graph of inequalities is as shown.