Question

If the lines y = 3x + 1 and 2y = x+ 3 are equally inclined to the line y = mx + 4, find the value of m.

Answer 1

here is Ur answer.....just that the answer after solving the equation is coming in decimals....and remember to use mod..

Answer 2

AnswEr:

Let $\theta$ be the acute angle which the line y = mx + 4 makes with the lines y = 3x + 1 and 2y = 3x + 3. Then,

$\qquad \sf \tan \theta = | \frac{m - 3}{1 + 3m} | \: \: and \\ \\ \qquad \sf \tan \theta = | \frac{m - \frac{1}{2} }{1 + \frac{m}{2} } | \\ \\ \rightarrow \sf \: | \frac{m - 3}{1 + 3m} | = | \frac{2m - 1}{m + 2} | \\ \\ \rightarrow \sf \: \frac{m - 3}{3m + 1} = \underline + \: \frac{2m - 1}{m + 2} \\ \\ \rightarrow \sf \: {m}^{2} - m - 6 = \underline + \: (6 {m}^{2} - m - 1) \\ \\ \rightarrow \sf \: 5 {m}^{2} + 5 = 0 \: \: \: or \\ 7 {m}^{2} - 2m - 7 = 0 \\ \\ \sf \rightarrow \: 7 {m}^{2} - 2m - 7 = 0 \\ \\ \sf \rightarrow \: m = \frac{1 \: \underline + \: 5 \sqrt{2} }{7}$

Therefore, value of m will 1 ± 5√2 / 7.