To know if an ordered pair satisfy an equation we have to substitute the values in it and see if the left side is equatl to the right side.
Pair (-2,10)
In this case x=-2 and y=10. Plugging the values in the equation:
[tex]\begin{gathered} 10=-3(-2)+4 \\ 10=6+4 \\ 10=10 \end{gathered}[/tex]since both sides have the same value, this paired satisfy the equation.
Pair (-1,1)
In this case x=-1 and y=1. Then
[tex]\begin{gathered} 1=-3(-1)+4 \\ 1=3+4 \\ 1=7 \end{gathered}[/tex]since this is not true, this ordered pair don't satisfy the equation.
Pair (5,-11)
In this case x=5 and y=-11. Then
[tex]\begin{gathered} -11=-3(5)+4 \\ -11=-15+4 \\ -11=-11 \end{gathered}[/tex]since this is true the ordered pair satisfy the equation.
Pair (6,-22)
In this case x=6 and y=-22. Then
[tex]\begin{gathered} -22=-3(6)+4 \\ -22=-18+4 \\ -22=-14 \end{gathered}[/tex]since this is not true, this ordered pair don't satisfy the equation.
Therefore the ordered pairs that satisfy the equation are the points A and C.
