Q 326 - Intermediate Algebra

Question

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

Step-by-Step Solution

Answer

The graph  is shown below

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