Answer:
Option C.
Step-by-step explanation:
A dashed straight line has a negative slope and goes through (0, 2) and (4, 0).
The given inequality is
[tex]y<-\dfrac{1}{2}x+2[/tex]
We need find the point which is a solution to the given linear inequality.
Check the given inequality for point (2, 3).
[tex]3<-\dfrac{1}{2}(2)+2[/tex]
[tex]3<1[/tex]
This statement is false. Option 1 is incorrect.
Check the given inequality for point (2, 1).
[tex]1<-\dfrac{1}{2}(2)+2[/tex]
[tex]1<1[/tex]
This statement is false. Option 2 is incorrect.
Check the given inequality for point (3, -2).
[tex]-2<-\dfrac{1}{2}(3)+2[/tex]
[tex]-2<0.5[/tex]
This statement is false. Option 3 is correct.
Check the given inequality for point (-1,3).
[tex]3<-\dfrac{1}{2}(1)+2[/tex]
[tex]3<1.5[/tex]
This statement is false. Option 4 is incorrect.
Therefore, the correct option is C.
