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