Answer:
Observe the attached image
Step-by-step explanation:
The limit of inequality is marked by the equation of the line
[tex]y = \frac{1}{3}x +\frac{1}{2}[/tex]
Therefore the first step to graph the inequality is to graph the line
[tex]y = \frac{1}{3}x +\frac{1}{2}[/tex]
First we find its cut point with the x axis. (y = 0)
[tex]0 = \frac{1}{3}x +\frac{1}{2}[/tex]
[tex]-\frac{1}{2}= \frac{1}{3}x[/tex]
[tex]x =\frac{-\frac{1}{2}}{\frac{1}{3}}\\\\x = -\frac{3}{2}[/tex]
Second we find its cut point with the y axis. (x = 0)
[tex]y= \frac{1}{3}(0) +\frac{1}{2}[/tex]
[tex]y =\frac{1}{2}[/tex]
Now that we know the cut points, we can graph the line.
Then, the inequality
[tex]y <\frac{1}{3}x +\frac{1}{2}[/tex]
it tells us that the region is made up of all the values of y that are smaller or that are below the equation of the line [tex]y = \frac{1}{3}x +\frac{1}{2}[/tex].
In this way we shadow the region that is below the line and this will be the graph of the inequality. Observe the attached image
