parallel lines = same slope
perpendicular lines = negative reciprocal slopes
since slope m = 2 the perpendicular slope will be -1/2
therefore all lines where y = -1/2x + b will be perpendicular
from here one could use a couple different line formulas. I'll start with the slope formula (since I have that memorized)
m = (y2 - y1)/(x2 - x1); which is easily changed to the point-slope formula by multiplying both sides by (x2 - x1):
(x2 - x1)m = (y2 - y1), or more simply: (x - x1)m = (y - y1).
The point-slope formula, as its name suggests, finds the equation of a line when both a point on the line and the slope are known.
The "point" of this point-slope formula is (3,4) and the slope is -1/2. Therefore, substituting in:
(x - 3)(-1/2) = (y - 4)
distribute the -1/2
-1/2x + 1.5 = y - 4
add 4 to both sides
-1/2x + 5.5 = y
and that's the equation:
y = -1/2x + 5.5
