Question

Write an equation of a line perpendicular to y=2x+3 and passes through (3,4).

Answer 1

Slope of the given line is 2 , therefore the slope of the perpendicular line is -(1/2)
Use your point slope equation y -y =m(x - x)

Y - 4 = -(1/2)(x - 3)
2(y - 4) = -1(x - 3). You are looking a proportion and cross multiplying
2y - 8 = -1x + 3
2y. =. -1x + 11
y. = -(1/2)x + (11/2)

Answer 2

perpendicular to y = 2x + 3 implies the new equation must be
y = (-1/2)x + b

sub in the point (3,4)
4 = (-1/2)(3) + b
b = 4 + 3/2 = 11/2

y = (-1/2)x + 11/2