which of the points is on the line segment with endpoints [-3,-8] and [3,10]?

Answer 1

which of what points?

The points that would be correct (and probably on your list) are:
Slope is 3
(-3,-8)
(-2,-5)
(-1,-2)
(0,1)
(1,4)
(2,7)
(3,10)

Answer 2

You have not mentioned which points you want to know. So here is the solution which can enable you to check if any point you can dream of lies on the the line segment with the end points mentioned by you.

A straight line is defined by the general equation: Y-Y1 = M(X-X1)
Your first end point can be labelled as follows: X1 = -3, Y1=-8
Your second end point can be X2 = 3 and Y2 = 10

So M = (Y2-Y1)/(X2-X1) = [10-(-8)]/[3-(-3)] = 3
Now simply subsitute X1,Y1,M into your general eqution:
Y-(-8) = 3[X-(-3)]
Y+8 = 3(X+3)
Y=3X+9-8
Y=3X+1. ----> This is the equation that describes your line segment.

Now lets say you want to check if [5,7] is on your line segment with the endpoints you mention. So X = 5 and Y=7 should be subsituted in Y=3X+1 as follows.

Y = 3X+1
7=3(5)+1
7 = 16 ----> This is not true! 7 is not equal to 16, so [5,7] does not lie on your line segment.

[2,7] lies on the line segment because:
Y=3X+1
7=3(2)+1
7=7. ----> This is true. So [2,7] lies on your line segment.

This way you can check any coordinate in the universe to see if it lies on your line segment or not.

Answer 3

Based on the data you have provided, I would have to say the answer is "None of the above"