through: (3, 2), perp. to y = -34x + 3

Answer 1

(y-2)/(x-3) = 1/34 in point slope form

cross multiply

34y - 68 = x -3

34y -x = 65

BUT it looks like you changed the problem to y= -(3/4)x + 3

then the perpendicular line has slope which is the negative inverse or +4/3

y=4x/3 + b, plug in the point (3,2) to find b

2 = 4(3)/3 + b

b = 2-4 =-2

y= (-4/3)x -2 is the perpendicular line through the given point (3,2)

BUT actually the way you wrote the equation in a comment

you really wrote y= -3/4x + 3 which is not a line, but a hyperbolic curve

y' = slope = (-3/4x)' = (3/4)x^-2 = 3/4x^2

at the point (3,2) the slope = 3/4(3)^2 = 1/12

but (3,2) isn't a point on the hyperbola so that probably isn't what you intended as the equation, as it's contradictory.

Technically though, when you write -3/4x it means -3/(4x) not (-3/4)x

PEMDAS means M before D, multiplication before division. 4x first, then divide it into -3, not divide first -3/4 then multiply that by x