It is given that the gradient of the line passing through a(2,1) and b(5,k) is 1/6. find the value of k.

Slope (gradient) : (y2 - y1) / (x2 - x1)
(2,1)..x1 = 2 and y1 = 1
(5,k)..x2 = 5 and y2 = k

slope : (k - 1) / (5 - 2) = 1/6
            (k - 1) / 3 = 1/6
            k - 1 = 1/6 * 3
            k - 1 = 1/2
            k = 1/2 + 1
            k = 1/2 + 2/2
            k = 3/2 or 1.5

check..
(3/2 - 1) / (5 - 2) = 1/6
(3/2 - 2/2) / 3 = 1/6
(1/2) / 3 = 1/6
1/2 = 1/6 * 3
1/2 = 3/6
1/2 = 1/2 (correct)

k = 3/2 or 1.5