Given that (5, 2), (-4, k) and (2, 1) lie on a straight line, find the value of k.
Explanation
(5, 2), (-4, k), (2, 1)
A straight line has constant gradient.
(frac{k – 2}{-4 – 5} = frac{1 – k}{2 – (-4)})
(frac{k – 2}{-9} = frac{1 – k}{6})
(-9(1 – k) = 6(k – 2) implies -9 + 9k = 6k – 12)
(9k – 6k = -12 + 9 implies 3k = -3)
(k = -1)