Question

If $\theta$ is an acute angle between the lines $y=2x+3,y=x+1$, then the value of $\tan \theta =$

• A. $2/3$
• B. $1/3$
• C. $3/4$
• D. $1/2$

Answer 1

The correct option is B $1/3$

If we have two lines $y=m_{1}x+c_1$ and $y=m_{2}x+c_2$

$\tan \theta =\left|\frac{m_1-m_2}{1+m_1{m}_2}\right|$

for $y=2x+3;m_1=2y=x+1;m_2=1$

$\therefore \tan \theta =\left|\frac{2-1}{1+2\times 1}\right|\tan \theta =\left|\frac{1}{3}\right|$

we need the acute angle so

$\tan \theta =\frac{1}{3}$