Answer :
Option B: [tex](-3,-12)[/tex]
Option E: [tex](0,0)[/tex]
Explanation:
The inequality is [tex]y<2 x+6[/tex]
Now, we shall determine the ordered pairs which satisfy the inequality.
Option A: [tex](-1,8)[/tex]
Substituting, the coordinate [tex](-1,8)[/tex] in the inequality [tex]y<2 x+6[/tex], we get,
[tex]8<2(-1)+6\\8<-2+6\\8<4[/tex]
This is not possible.
Hence, the ordered pair [tex](-1,8)[/tex] does not satisfy the inequality.
Option A is not the correct answer.
Option B: [tex](-3,-12)[/tex]
Substituting, the coordinate [tex](-3,-12)[/tex] in the inequality [tex]y<2 x+6[/tex], we get,
[tex]-12<2(-3)+6\\-12<-6+6\\-12<0[/tex]
This is possible.
Hence, the ordered pair [tex](-1,8)[/tex] satisfy the inequality.
Option B is the correct answer.
Option C: [tex](0,12)[/tex]
Substituting, the coordinate [tex](0,12)[/tex] in the inequality [tex]y<2 x+6[/tex], we get,
[tex]12<2(0)+6\\12<0+6\\12<6[/tex]
This is not possible.
Hence, the ordered pair [tex](0,12)[/tex] does not satisfy the inequality.
Option C is not the correct answer.
Option D: [tex](-2,10)[/tex]
Substituting, the coordinate [tex](-2,10)[/tex] in the inequality [tex]y<2 x+6[/tex], we get,
[tex]10<2(-2)+6\\10<-4+6\\10<2[/tex]
This is not possible.
Hence, the ordered pair [tex](-2,10)[/tex] does not satisfy the inequality.
Option D is not the correct answer.
Option E: [tex](0,0)[/tex]
Substituting, the coordinate [tex](0,0)[/tex] in the inequality [tex]y<2 x+6[/tex], we get,
[tex]0<2(0)+6\\0<0+6\\0<6[/tex]
This is possible.
Hence, the ordered pair [tex](0,0)[/tex] satisfy the inequality.
Option E is the correct answer.