# Find equation of line that is perpendicular to the tangent line to the curve

## Homework Statement

Find the equation of the line that is perpendicular to the tangent line to the curve, y=(3x+1)/(4x-2) at the point (1,2)

## The Attempt at a Solution

I am absolutely confused with this problem. I tried taking a derivative of the equation. And I got y'=-10/(4x-2)2
I couldn't set it equal to 0, it will not work. What have I done wrong?

There's no need to solve -10/(4x-2)2 = 0 because you're not supposed to find when/if the tangent line to the curve is ever horizontal. The problem wants you to first find the slope of the tangent line at the point (1, 2); you need to find the derivative when x = 1.

Excuse me, what exactly do you mean by that?

Dick
Homework Helper
y'(x) is the slope of the tangent line. Substitute x=1 into your equation for y'(x) to find the slope of the tangent line. What's y'(1)? Now what's the relation between the slope of the tangent line and a perpendicular to it?

y'(x) is the slope of the tangent line. Substitute x=1 into your equation for y'(x) to find the slope of the tangent line. What's y'(1)? Now what's the relation between the slope of the tangent line and a perpendicular to it?

OK, here we go:

y'(1)=-10/4

Normal line is reciprocal of the tangent, which is 4/10.
The normal line equation is:

y-2=0.4(x-1)
y=0.4x+1.6

Dick
Homework Helper
OK, here we go:

y'(1)=-10/4

Normal line is reciprocal of the tangent, which is 4/10.
The normal line equation is:

y-2=0.4(x-1)
y=0.4x+1.6

Uh, NEGATIVE reciprocal of the tangent. Works for me. Seem ok to you?

Uh, NEGATIVE reciprocal of the tangent. Works for me. Seem ok to you?

That's what I exactly meant Thank you SO much for everything.