Answer:
Option B) {(1, -1), (-3, -3), (2, 4)}
Step-by-step explanation:
The correct inequality is
[tex]y>\frac{1}{2}x-2[/tex]
The solution of the inequality is the shaded area above the dashed line [tex]y=\frac{1}{2}x-2[/tex]
see the attached figure to better understand the problem
we know that
If a ordered pair satisfy the inequality, then the ordered pair must lie in the shaded area of the solution
Verify each case
case A) {(6, 1), (-1, -3), (4, 4)}
ordered pair (6,1)
For x=6, y=1
substitute in the inequality
[tex]1>\frac{1}{2}(6)-2[/tex]
[tex]1>1[/tex] ---> is not true
therefore
The point not satisfy the inequality
case B) {(1, -1), (-3, -3), (2, 4)}
ordered pair (1,-1)
For x=1, y=-1
substitute in the inequality
[tex]-1>\frac{1}{2}(1)-2[/tex]
[tex]-1>-1.5[/tex] ---> is true
so
The point satisfy the inequality
ordered pair (-3,3)
For x=-3, y=3
substitute in the inequality
[tex]3>\frac{1}{2}(-3)-2[/tex]
[tex]3>-3.5[/tex] ---> is true
so
The point satisfy the inequality
ordered pair (2,4)
For x=2, y=4
substitute in the inequality
[tex]4>\frac{1}{2}(2)-2[/tex]
[tex]4>-1[/tex] ---> is true
so
The point satisfy the inequality
therefore
The set contains only points that satisfy the inequality
case C) {(1, -1), (-3, -3), (4, -2)}
ordered pair (4,-2)
For x=4, y=-2
substitute in the inequality
[tex]-2>\frac{1}{2}(4)-2[/tex]
[tex]-2>0[/tex] ---> is not true
therefore
The point not satisfy the inequality
case D) {(-1, -3), (-3, -3), (2, 4)}
ordered pair (-1,-3)
For x=-1, y=-3
substitute in the inequality
[tex]-3>\frac{1}{2}(-1)-2[/tex]
[tex]-3>-2.5[/tex] ---> is not true
therefore
The point not satisfy the inequality
