Part A) Notice that the given inequality is an inclusive inequality, therefore the boundary of its solution set is a solid line.
The equation that represents the boundary of the solution set to the given inequality is:
[tex]y+x=1.[/tex]
Setting x=0 in the above equation we get:
[tex]\begin{gathered} y+0=1, \\ y=1. \end{gathered}[/tex]
Therefore the boundary passes through (0,1)
Setting y=0 in y+x=1 we get:
[tex]\begin{gathered} 0+x=1, \\ x=1. \end{gathered}[/tex]
Therefore the boundary passes through (1,0).
Then the graph of the boundary of the given inequality is:
Part B) Notice that:
[tex]1+1=2\geq1.[/tex]
Therefore the point (1,1) is part of the solution set to the given inequality.
Answer:
