To graph the inequality:
[tex]6x-2y>-11[/tex]We use the x and y-intercepts.
When x=0
[tex]\begin{gathered} 6x-2y>-11 \\ 6(0)-2y>-11 \\ -2y>-11 \\ \frac{-2y}{-2}<\frac{-11}{-2} \\ y<5.5 \end{gathered}[/tex]We have the point: (0, 5.5)
When y=0
[tex]\begin{gathered} 6x-2y>-11 \\ 6x>-11 \\ x>\frac{-11}{6} \\ x>-1.83 \end{gathered}[/tex]We have the point: (-1.83, 0)
We plot the points (0, 5.5) and (-1.83,0).
The points are joined using a broken line because of the inequality sign: >
The graph is shown below:
To determine which side is required, we use the origin test.
When x=0 and y=0
[tex]\begin{gathered} 6x-2y>-11 \\ 0>-11\text{ (TRUE)} \end{gathered}[/tex]This means the side of the line containing (0,0) is where we need. (Shaded above)
