Normal Line to a Tangent
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Finding the Equation of a Normal
by
Eddie W.
Key Questions

A normal line is the line perpendicular to a tangent line at the point of contact.

If a tangent line has the equation
#yy_1=m(xx_1)# ,then the normal line at the point of contact is
#yy_1=1/m(xx_1)# .
I hope that this was helpful.

The normal line is the line that is perpendicular to the the tangent line.
If the slope of a line is
#m# then the slope of the perpendicular line is#1/m# , this is also known as the negative reciprocal.The given equation is
#y=5/6x9# the slope is#5/6# so the slope of the normal is#6/5# .The point
#(x,y)>(4,8)# #y=mx+b ># Substitute in the values of#m# ,#x# and#y# #8=6/5(4)+b# #8=24/5+b# #24/5+8=b# #24/5+40/5=b# #64/5=b# The equation of the normal line is
#> y=6/5x+64/5#
Questions
Videos on topic View all (6)
Derivatives

1Tangent Line to a Curve

2Normal Line to a Tangent

3Slope of a Curve at a Point

4Average Velocity

5Instantaneous Velocity

6Limit Definition of Derivative

7First Principles Example 1: xÂ²

8First Principles Example 2: xÂ³

9First Principles Example 3: square root of x

10Standard Notation and Terminology

11Differentiable vs. Nondifferentiable Functions

12Rate of Change of a Function

13Average Rate of Change Over an Interval

14Instantaneous Rate of Change at a Point