Question

Graph the inequality $x-y\ge 3$. How do you know which side of the line $x-y=3$should be shaded?

Short answer

The graph is shown below

Step-by-step solution

Step 1. Given information

The given linear inequality is$x-y\ge 3$

Step 2. Calculation

$$\begin{gathered} \mathrm{Using}\mathrm{inequality}\mathrm{x}-\mathrm{y}\ge 3, \\ \mathrm{and}\mathrm{graphing}\mathrm{x}-\mathrm{y}=3\mathrm{and}\mathrm{testing}\mathrm{a}\mathrm{point}.\mathrm{And}\mathrm{the}\mathrm{boundary}\mathrm{will}\mathrm{be}\mathrm{solid}. \\ \mathrm{Now},\mathrm{Test}(0,0)\mathrm{which}\mathrm{makes}\mathrm{the}\mathrm{inequality}\mathrm{false}. \\ \mathrm{So}\mathrm{shade}\left(\mathrm{Blue}\right)\mathrm{side}\mathrm{that}\mathrm{does}\mathrm{not}\mathrm{contain}(0,0). \end{gathered}$$

Step 3. The graph obtained