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.
\(\frac{k - 2}{-4 - 5} = \frac{1 - k}{2 - (-4)}\)
\(\frac{k - 2}{-9} = \frac{1 - k}{6}\)
\(-9(1 - k) = 6(k - 2) \implies -9 + 9k = 6k - 12\)
\(9k - 6k = -12 + 9 \implies 3k = -3\)
\(k = -1\)