Question

If the angle between two lines pi/4 and slope of one of the lines is 1/2 , find the slope of the other line.

Answer 1

Slope of another line = 3  or -1/3

Step-by-step explanation:

angle between two lines π/4

slope of one of the lines is 1/2

slope of other line = m

Tan (π/4)  = | (m - 1/2) / (1  + m(1/2)|

=> 1  =  | (2m - 1)/( 2 + m) |

case 1

(2m - 1)/(2 + m) = 1

=> 2m - 1 = 2 + m

=> m = 3

case 2

(2m - 1)/(2 + m) = -1

=> 2m - 1 = -2 - m

=> 3m = -1

=> m = -1/3

Learn more:

if the angle between the lines kx + y + 9 = 0, y - 3x = 4 is 45° the ...

https://brainly.in/question/14041873

Derive an expression for acute angle between two lines slopes m1 ...

https://brainly.in/question/12863695

Answer 2

$\Large{\textbf{\underline{\underline{According\:to\:the\:Question}}}}$

As we already know that :-

θ b/w two lines having slopes m1 and m2

Hence,

${\boxed{\sf\:{tan\theta=|\dfrac{m_{2}-m_{1}}{1+m_{1}m{2}}..... (1)}}}$

Assume,

${\boxed{\sf\:{m_{1}=\dfrac{1}{2}}}}$

${\boxed{\sf\:{m_{2}=m}}}$

${\boxed{\sf\:{\theta=\dfrac{\pi}{4}}}}$

$\textbf{\underline{Substituting\;value\;in\;(1)}}$

${\boxed{\sf\:{|\dfrac{m-1/2}{1+1/2m}|=\dfrac{\pi}{4}}}}$

${\boxed{\sf\:{|\dfrac{2m-1}{2+m}|=1}}}$

${\boxed{\sf\:{\dfrac{2m-1}{2+m}=\pm 1}}}$

${\boxed{\sf\:{\dfrac{2m-1}{2+m}=1}}}$

${\boxed{\sf\:{\dfrac{2m-1}{2+m}=-1}}}$

(2m - 1) = (2 + m)

(2m - 1) = (-2 - m)

m = 3

${\boxed{\sf\:{m=\dfrac{-1}{3}}}}$

Slope

${\boxed{\sf\:{3\;or\; \dfrac{-1}{3}}}}$