Question

In Problems 44 and 45, graph each inequality by hand. Verify your results using a graphing utility.

$3x+4y\le 12$

Short answer

The graph of$3x+4y\le 12$is

Step-by-step solution

Step 1. Given data

The given inequality is

$3x+4y\le 12$

Step 2. Properties of the graph of the inequality

Graph of $3x+4y=12$will be a line

now test the point $(0,0)$inequality

$$\begin{gathered} 3x+4y\le 12 \\ 3\left(0\right)+4\left(0\right)\le 12 \\ 0\le 12 \end{gathered}$$

inequality satisfied so the point $(0,0)$will lie in the region of inequality

So shade the region from line role="math" localid="1646954411324" $3x+4y=12$toward the origin

Step 3. graph of the inequality 

Plot a solid line $3x+4y=12$and shade the region toward origin to plot the graph of$3x+4y\le 12$

Step 4. Verification

Plot the graph of$3x+4y\le 12$using a graphing utility

Graph matches with our graph so our graph is correct.