The graph of an absolute value parent function is a pair of rays in quadrant 1 & 2, as shown in the graph.
The absolute value function is
f(x) = |x| or y = |x|
We also know that the absolute function can be wriiten as
y = |x|
=> y = x or y = -x
Comparing with y = mx + c
We get
m = 1 or m=-1 and c = 0
c = 0 implies that the line passes through the origin.
Hence the slopes shall be -1, 1 & the line passes through the origin.
Option A, B & D are the right answers.
(1,9) (-3,5)
Midpoint = (1+{-3}/2) (9+5/2)
(1-3/2) (14/2)
(-2/2) (7)
(-1) (7)
Midpoint Answer = (-1, 7)