Chapter 11, Problem 79RE

To determine

Graph each inequality.

Answer to Problem 79RE

Explanation of Solution

Given information:

Graph each inequality.

  $3x+4y\le 12$

Calculation:

To graph the given inequality, first graph the line $3x+4y=12$ using solid line since the inequality is nonstrict.

Use a test point, say $\left(0,0\right)$ , and determine the part of the graph to be shaded.

Substitute $0$ for $x$ and $y$ in the inequality $3x+4y\le 12$ .

  $3\left(0\right)+4\left(0\right)\le 12$

  $0<12$

The point $\left(0,0\right)$ satisfies the inequality. So, we shade the part below the line.

Hence, the shaded region represents the given inequality.