Two lines are parallel if their slopes are identical. For this exercise, we have been given two points on each line, so we have enough information to calculate their slopes using the Slope Formula.
m=y_2- y_1/x_2- x_1
Note that when choosing points to substitute for ( x_1, y_1) and ( x_2, y_2), it does not matter which points on the line we choose, since the result will be the same.
Line
Points
y_2-y_1/x_2-x_1
Slope
Simplified Slope
a
( -5, 3) & ( -6, -1)
-1- 3/-6-( -5)
-4/-1
4
b
( 3, -2) & ( 2, -7)
-7-( -2)/2- 3
-5/-1
5
Now that we have identified the slope of each line, we can see that the lines do not have the same slope, so they are not parallel.
