Question

Graph the inequality on the axes below.y < 1/2x + 1

Answer 1

Write out the given inequality

`y\: <\: 1/2x\: +\: 1`

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

`y=(1)/(2)x+1`

Step 2: Obtain the intercept on both asix, we have

`\begin{gathered} \text{for x-intercept, put y=0} \\ 0=(1)/(2)x+1 \\ -(1)/(2)x=1 \\ \text{Multiply both sides by -2, we have } \\ x=-2 \\ (-2,0) \end{gathered}`

Then

`\begin{gathered} \text{for y-intercept, put x=0} \\ y=(1)/(2)(0)+1 \\ \text{Hence} \\ y=1 \\ (1,0) \end{gathered}`

Step3: Then join the two point using dotted line since an equal sign is not inviolve in the inequality symbol

Hence, we have