Chapter 6.5, Problem 17PPS

To determine

Graph the inequality $2x+3y\ge 18$ .

Explanation of Solution

Given:

The inequality is $2x+3y\ge 18$ .

Calculation:

Simplify the inequality as follows:

  $\begin{array}{l}2x+3y\ge 18\\ 2x-2x+3y\ge -2x+18\\ \frac{3y}{3}\ge \frac{-2x}{3}+\frac{18}{3}\\ y\ge \frac{-2}{3}x+6\mathrm{......}\left(1\right)\end{array}$

Thus, the graph of $y=\frac{-2}{3}x+6$ ,

Consider x = 0,

  $\begin{array}{l}y=\frac{-2}{3}\left(0\right)+6\\ y=6\end{array}$

Thus, the coordinate is (0, 6).

Consider y = 0,

  $\begin{array}{c}\left(0\right)=\frac{-2}{3}x+6\\ x=9\end{array}$

Thus, the coordinate is (9, 0).

The graph of the line is shown below:

  

Apply the inequality in the graph on the upward of the graph as inequality is greater than equal to in equation (1).