Answer:
The graph is represented below.
Step-by-step explanation:
Given:
The inequality to graph is given as:
[tex]y<\frac{x}{2}-3[/tex]
In order to graph it, we first graph the line. So, we replace the inequality sign by equal to sign. This gives,
[tex]y=\frac{x}{2}-3[/tex]
Now, let [tex]x=0[/tex]. So, the value of 'y' is given as:
[tex]y=\frac{0}{2}-3=-3[/tex]
A point on the line is (0, -3)
Now, let [tex]y=0[/tex]. So, the value of 'x' is given as:
[tex]0=\frac{x}{2}-3\\\\\frac{x}{2}=3\\\\x=6[/tex]
Another point on the line is (6, 0).
Now, mark the points on the graph and draw a line passing through these two points.
Now, we consider the inequality [tex]y<\frac{x}{2}-3[/tex].
As 'y' is less than [tex]\frac{x}{2}-3[/tex], so the solution region is the region below the line as shown in the graph below.
Also, the line itself is not included in the solution. So, the line is a broken line and not a continuous line.
