Two straight lines are parallel if the slope of both of them is the same. The slope of a line passing through (x1, y1) and (x2, y2) is given by (y2 - y1)/(x2 - x1)
Here we have line passing through (-1,1) and (5,2), and through (-1,4) and (2,3).
The slope of the line through (-1,1) and (5,2) is (2 -1)/(5+1) = 1/6
That of the line through (-1,4) and (2,3) is ( 4 - 3)/(-1 -2) = -1/3
As the slope is not the same, the lines are not parallel.
Since we know the points through the lines are passing, we'll calculate the slopes.
Slope of line through the points (-1,1) and (5,2) is:
m1 = (2-1)/(5+1)
m1 = 1/6
Now, we'll consider the next two points (-1,4) and (2,3).
m2 = (3-4)/(2+1)
m2 = 1/3
We know that 2 lines are parallel if their slopes are equal.
m1 is different from m2.
Therefore, the given lines are not parallel.