Chapter 7.7, Problem 55E

To determine

To calculate: Graph the inequality in a coordinate plane $8x\le 4y-12$ .

Answer to Problem 55E

Graph is closed half plane which does not contain origin.

  

Explanation of Solution

Given information: The given inequality in a coordinate plane is $8x\le 4y-12$ .

Calculation: $8x\le 4y-12$

Corresponding equation is

  $\begin{array}{l}8x=4y-12\\ \mathrm{when}x=0\\ 0=4y-12\\ 12=4y\\ \frac{12}{4}=y\\ 3=y\\ \mathrm{when}y=0\\ 8x=4(0)-12\\ 8x=-12\\ x=\frac{-12}{8}=\frac{-3}{2}\\ \left(0,3\right)\mathrm{and}\left(\frac{-3}{2},0\right)\end{array}$

  $\left(0,3\right)\mathrm{and}\left(\frac{-3}{2},0\right)$ lie on the line.

  

Put $x=0$ and $y=0$ in given equation

  $\begin{array}{l}0\le 0-12\\ 0\le -12\end{array}$

Which is false.

Therefore graph is closed half plane which does not contain origin.