To graph the inequality, we can do the following steps.
Step 1: We rearrange the equation so y is on the left and everything else is on the right.
[tex]\begin{gathered} x-2y\le0 \\ \text{ Subtract x from both sides} \\ x-2y-x\le0-x \\ -2y\le-x \\ \text{ Divide by -2 from both sides} \\ \frac{-2y}{-2}\le\frac{-x}{-2} \\ y\ge\frac{x}{2} \end{gathered}[/tex]Step 2: We plot the line associated with the inequality. For this, we choose two values of x and replace them in the below equation.
[tex]\begin{gathered} x=2 \\ $\boldsymbol{y=\frac{x}{2}}$ \\ y=\frac{2}{2} \\ y=1 \\ \text{ Then, the lines passes through the point (2,1).} \end{gathered}[/tex][tex]\begin{gathered} x=4 \\ y=\frac{x}{2} \\ y=\frac{4}{2} \\ y=2 \\ \text{ Then, the lines passes through the point (4,2).} \end{gathered}[/tex]Since inequality has the symbol ≥, we make a solid line.
Step 3: Since inequality has the symbol ≥, we shade above the line. Therefore, the graph of the inequality is:
