The choices were not given but same question was retrieved from another source with the following choices: (2,1), (2,4), (2,6), (2,9).
The most accurate way to verify if a point lies on the graph of the equation containing (3, 11) and (-2, 1) is to actually find the eqution first.
For this, we need the points' slope, m, which is basically the rate of the difference of the y values over the x values. For this case, it's
m = (11 - 1)/ (3 - -2) = 10/5 = 2
Now that we have the slope, we can write the general equation as
(y - y1) = m(x- x1)
We can choose either of the points for x1 and y1. So, we now have
(y - 1) = 2(x - -2)
y -1 = 2x + 5
y = 2x + 5
Now that we have the equation, y = 2x + 5, we can check which of the given points satisfy this. Since each of the choices have 2 as the x-coordinate, we can substitute this and look for y.
y = 2(2) + 5 = 9
Therefore, the point lying in the same line is (2, 9).
