SOLUTION
Write out the given inequality
[tex]y\: <\: 1/2x\: +\: 1[/tex]
Then, to graph the inequality, we need to do the following
steps 1. Get the equation of the line
Change the iniequatity symbol to equals signed
[tex]y=\frac{1}{2}x+1[/tex]
Step 2: Obtain the intercept on both asix, we have
[tex]\begin{gathered} \text{for x-intercept, put y=0} \\ 0=\frac{1}{2}x+1 \\ -\frac{1}{2}x=1 \\ \text{Multiply both sides by -2, we have } \\ x=-2 \\ (-2,0) \end{gathered}[/tex]
Then
[tex]\begin{gathered} \text{for y-intercept, put x=0} \\ y=\frac{1}{2}(0)+1 \\ \text{Hence} \\ y=1 \\ (1,0) \end{gathered}[/tex]
Step3: Then join the two point using dotted line since an equal sign is not inviolve in the inequality symbol
Hence, we have
