2 questions about parallel and perpendicular lines

Find a given that the line joining P(a, -3) to Q(4, -2) is parallel to line with gradient 1/3.

Find t given that the line joining P(t, -2) to Q(5, t) is perpendicular to a line with slope -1/4

slope = (y1 - y2)/(x1 - x2) where (x1,y1) and (x2,y2) are two points the line goes through
1) Parallel lines have equal slope so the line through P and Q has slope = 1/3
1/3 = (-3 - -2)/(a - 4)
1/3 = -1/(a - 4)
a - 4 = -3
a = 1
2) Perpendicular lines have slopes that are negative reciprocals of each other so the line through P and Q has slope = -1/(-1/4) = 4
4 = (-2 - t)/(t - 5)
4(t - 5) = -2 - t
4t - 20 = -2 - t
5t = 18
t = 18/5

"Find a given that the line joining P(a, -3) to Q(4, -2) is parallel to line with gradient 1/3."
Gradient of a straight line is (y1-y2)/(x1-x2), so:
(-3 - -2)/(a - 4) = 1/3
-1/(a - 4) = 1/3
-(a - 4) = 3
4 - a = 3
a = 1

"Find t given that the line joining P(t, -2) to Q(5, t) is perpendicular to a line with slope -1/4"
To get a gradient perpendicular to another, take its negative reciprocal, so in this case the gradient we need is 4.

(-2 - t)/(t-5) = 4
-2 - t = 4t - 20
18 = 3t
t = 6