Find the slope of the line which makes an angle pi/4 with the line x-2y+5 (no links please) - Maths - Straight Lines

Question

Find the slope of the line which makes an angle pi/4 with the line
x-2y+5 (no links please)

Lovina Kansal · Accepted Answer

Dear student
Let the slope of the required line be m
The equation of the given  line is x-2y+5=0    
(1)⇒y=x+52Slopeof line (1) is 12The angle between the line is 45°If the slope of two lines are m1 and mwand the angle between them is θ
Thentanθ=m1-m21+m1m2⇒tan45°=12-m21+m22⇒1=1-2m22+m2⇒1-2m22+m2=±1⇒1-2m22+m2=1 or1-2m22+m2=-1⇒1-2m2=2+m2 or 1-2m2=-2-m2⇒3m2=-1 or m2=3⇒m2=-13 or m2=3
Regards