Find a general equation of a line L which passes through B0

Find a general equation of a line L which passes through B(0, 1), and has a direction vector that points in the N45E direction.

Solution

direction vecot is N45^oE ==> < cos(90^o -45^o) , sin(90^o -45^o) >

==> < cos(45^o) , sin(45^o) >

==> <1/2 , 1/2>

Slope of line m = y/x = (1/2)/(1/2)

==> Slope m = 1

equation of line with slope m and passing through (x₁ , y₁) is y - y₁ = m(x - x₁)

here m = 1 , (x₁ , y₁) = (0 , 1)

y - 1 = 1(x - 0)

==> y - 1 = x

==> y = x +1

Hence equation of required line is y = x +1