Question

) Find the acute angle between the lines y = 5x + 6 and y = x

Answer 1

Heyy....
Answer is here....
see picture...

Answer 2

Answer:

The angle between them is $\theta=33.69^\circ$    

Step-by-step explanation:

Given : Equation $y=5x+6$ and $y=x$.

To find : The acute angle between the lines ?

Solution :

First we find the slope of the equation.

The general slope form is y=mx+c

Where, m is the slope of the equation.

On comparing, $y=5x+6$

The slope is $m_1=5$

On comparing, $y=x$

The slope is $m_2=1$

The formula to find angle between lines is

$\tan\theta=|\frac{m_1-m_2}{1+m_1m_2}|$

Substituting the values we get,

$\tan\theta=|\frac{5-1}{1+5\times 1}|$

$\tan\theta=|\frac{4}{1+5}|$

$\tan\theta=|\frac{4}{6}|$

$\tan\theta=|\frac{2}{3}|$

$\theta=\tan^{-1}(\frac{2}{3})$

$\theta=33.69^\circ$

Therefore, The angle between them is $\theta=33.69^\circ$