Solution:
To graph, a linear inequality in two variables (say, x and y ), first get y alone on one side. Then consider the related equation obtained by changing the inequality sign to an equals sign. The graph of this equation is a line.
If the inequality is strict ( < or > ), graph a dashed line. If the inequality is not strict ( ≤ and ≥ ), graph a solid line.
For example,
Consider the linear inequality in two variables below
[tex]y\leq4x-8[/tex]
Step 1:
Put x=0 and find y
[tex]\begin{gathered} y=4x-8 \\ y=4(0)-8 \\ y=0-8 \\ y=-8 \\ (0,-8) \end{gathered}[/tex]
Step 2:
Put y=0 and find x
[tex]\begin{gathered} y=4x-8 \\ 0=4x-8 \\ 4x=8 \\ \frac{4x}{4}=\frac{8}{4} \\ x=2 \\ (2,0) \end{gathered}[/tex]
Hence,
We are going to use the coordinates below to graph the inequality using a solid line because
The inequality sign used is greater than or equal to
[tex](0,-8),(2,0)[/tex]
Hence,
The graph of the inequality will be
