NECO 2022 · Paper 1 · Q38

Find the acute angle between the lines $x + 4y = 12$ and $2y - x = -6$ .

Worked solution (try it first)

Make $y$ the subject of each: $y = -\frac{1}{4}x + 3$ and $y = \frac{1}{2}x - 3$ , so the gradients are $m_1 = -\frac{1}{4}$ and $m_2 = \frac{1}{2}$ .
Use $\tan\theta = \left|\dfrac{m_1 - m_2}{1 + m_1 m_2}\right|$ : the top is $-\frac{3}{4}$ and the bottom is $1 - \frac{1}{8} = \frac{7}{8}$ .
So $\tan\theta = \frac{3}{4} \div \frac{7}{8}$
$= \frac{6}{7}$ , and $\theta \approx 40.6^\circ$ , option B.