The given lines are
Line A: (1,5) and (-2,-4)
Line B: (3,2) and (1,-4)
Line C: (6,1) and (-4,2)
The first step is to determine the slope of each line. The formula for determining slope is expressed as
slope = (y2 - y1)/(x2 - x1)
Considering line A,
x1 = 1, y1 = 5
x2 = - 2, y2 = - 4
Slope = (- 4 - 5)/(- 2 - 1) = - 9/- 3
Slope = 3
Considering line B,
x1 = 3, y1 = 2
x2 = 1, y2 = - 4
Slope = (- 4 - 2)/(1 - 3 = - 6/- 2 =
Slope = 3
Considering line C,
x1 = 6, y1 = 1
x2 = - 4, y2 = 2
Slope = (2 - 1)/(- 4 - 6) = 1/- 10
Slope = 1/- 10
If two lines are parallel, it means that they have the same slope. We can see that the slopes of line A and B are equal. Thus,
Line A and line B are parallel