To graph an inequality, we can fisrt write the inequality solved by y:
[tex]\begin{gathered} x-y\le4 \\ -y\le4-x \\ y\ge x-4 \end{gathered}[/tex]
Now, we can first find the boundary part, that is, the graph of the equivalent equation:
[tex]y=x-4[/tex]
This is a line, so we can pick two points and connect them.
Let's use the points for x = 0 and x = 1:
[tex]\begin{gathered} x=0\colon \\ y=0-4=-4 \\ x=1\colon \\ y=1-4=-3 \end{gathered}[/tex]
So, we have points (0, -4) and (1, -3). So, the line for the equation is:
Now, to find the graph of the inequality, we can see that this is the boundary and we have the inequality sign ≥, that is greater than or equal to.
So, we want the y values that are on the line or above it, so the graph for the inequality is:
