Given that the straight lines \(kx - 5y + 6 = 0\) and \(mx +
FURTHER MATHEMATICS
WAEC 2007
Given that the straight lines \(kx - 5y + 6 = 0\) and \(mx + ny - 1 = 0\) are parallel, find a relationship connecting the constants m, n and k.
- A. 5n - km = 0
- B. kn + 5m = 0
- C. 5n + km = 0
- D. kn - 5m = 0
Correct Answer: B. kn + 5m = 0
Explanation
Two lines are parallel if and only if their slopes are equal.
\(kx - 5y + 6 = 0 \implies 5y = kx + 6\)
\(y = \frac{k}{5}x + \frac{6}{5}\)
\(Slope = \frac{k}{5}\)
\(mx + ny - 1 = 0 \implies ny = 1 - mx\)
\(y = \frac{1}{n} - \frac{m}{n}x\)
\(Slope = -\frac{m}{n}\)
\(Parallel \implies \frac{k}{5} = -\frac{m}{n}\)
\(-5m = kn \implies 5m + kn = 0\)
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