Right this is pretty simple all you do is sub the points to the equation given. So first try the first point (2,-1) in y=-3x+7 ==> -1=-3(2)+7 ==>-1=1 this is not equal therefore not the right points
Then try (1,10) ==>10=-3(1)+7 ==>10=4 this is incorrect therefore not the right points
Next try (3,-2) ==>-2=-3(3)+7 ==>-2=-2 this is equal therefore this is the coordinates to the linear equation.
Finally try the last points to make sure you are correct. ==> -8=-3(-5)+7 ==>-8=22 this is incorrect also.
Therefore the only coordinates that satisfies the equation is (3,-2)