R thse lnes parallel,perpendicular,or neither, The line thru (5,2)and (9,-3). The line thru (4,6)and (8,1)?

Question

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Answer 1

to determine whether two lines are parallel or perpendicular or neither, we need to have their slopes.
the slope of a line passing through (x1,y1) and (x2,y2) is given by m=(y2-y1)/(x2-x1)
two lines are parallel, if their slopes are equal
two lines are perpendicular if the product of their slopes is -1
first find the slopes of both the lines
slope of first line is m1=(-3-2)/(9-5)=(-5/4)
slope of the second line is m2=(1-6)/(8-4)=(-5/4)
since m1=m2, the lines are parallel, but not perpendicular

Answer 2

We know slope (m) of a line passing through points (x1,y1) and (x2,y2) is given by m = (y2-y1)/(x2-x1)
Therefore,
m1 = (-3-2)/(9-5) = -5/4
m2 = (1-6)/(8-4) = -5/4

Since m1 = m2
Thus these lines are parallel.

Answer 3

find the slopes of both the lines
by using the formula
m = (y2 -y1) / (x2 -x1)

if m1 = m2 Lines are parallel
if m1*m2 = -1 lines are perpendicular