We need to find the slope of the lines passing through each pair of point and see which category they fit in.
(-7, 3) and (-7, 11)
The slope is
[tex]\frac{11-3}{-7-(-7)}=\frac{8}{0}=\text{undefined}[/tex]
(2, 6) and (11, -3)
The slope is
[tex]\frac{-3-6}{11-2}=-\frac{9}{9}=-1[/tex]
(-2, 7) and (8. 7)
The slope of the line between these two points is
[tex]\frac{7-7}{8-(-2)}=0[/tex]
(2, 3) and (-3, 11)
The slope is
[tex]\frac{11-3}{-3-2}=\frac{8}{-5}[/tex]
(5, 1) and (8,5)
The slope is
[tex]\frac{5-1}{8-5}=\frac{4}{3}[/tex]
Having found the slope of lines between all pairs, we are now in a position to fill in the table.
(-7, 3) and (-7, 11) = undefined.
(2, 6) and (11, -3) = slope is negative
(-2, 7) and (8. 7) = slope is zero
(2, 3) and (-3, 11) = slope is negative
(5, 1) and (8,5 )= slope is positive.
