For x = 3, w = 6:
Line a: slope = -3/2
Line d: slope = -3/2
Since the slopes are equal, line a is parallel to line d for x = 3 and w = 6.
For x = 5, w = 3:
Line a: slope = 2/3
Line d: slope = -3/2
The slopes are not equal, so line a is not parallel to line d for x = 5 and w = 3.
For x = 1, w = 5:
Line a: slope = -5/1 = -5
Line d: slope = -3/2
The slopes are not equal, so line a is not parallel to line d for x = 1 and w = 5.
For x = 3, w = 5:
Line a: slope = -5/2
Line d: slope = -3/2
Since the slopes are equal, line a is parallel to line d for x = 3 and w = 5.
Therefore, line a is parallel to line d for x = 3, w = 6 and x = 3, w = 5.
However, line a is not parallel to line d for x = 5, w = 3 and x = 1, w = 5.
To summarize:
Line a is parallel to line d for x = 3, w = 6 and x = 3, w = 5.
Line a is not parallel to line d for x = 5, w = 3 and x = 1, w = 5.
To determine if two lines are parallel, we compare their slopes. If the slopes are equal, then the lines are parallel. If the slopes are not equal, then the lines are not parallel.
In this case, we are given the values of x and w and we need to determine if the lines are parallel for each given combination.
For the first combination, x = 3 and w = 6, we are given the slopes of line a and line d. The slope of line a is -3/2 and the slope of line d is also -3/2. Since the slopes are equal, we can conclude that line a is parallel to line d for x = 3 and w = 6.
For the second combination, x = 5 and w = 3, we again compare the slopes of line a and line d. The slope of line a is 2/3 and the slope of line d is -3/2. Since the slopes are not equal, we can conclude that line a is not parallel to line d for x = 5 and w = 3.
Similarly, for the third combination, x = 1 and w = 5, the slopes of line a and line d are -5 and -3/2 respectively. Again, the slopes are not equal, so line a is not parallel to line d for x = 1 and w = 5.
Finally, for the fourth combination, x = 3 and w = 5, the slopes of line a and line d are -5/2 and -3/2 respectively. Since the slopes are equal, we can conclude that line a is parallel to line d for x = 3 and w = 5.
Therefore, line a is parallel to line d for x = 3, w = 6 and x = 3, w = 5.