Normal Line to a Tangent
Key Questions

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

Tangent Line to a Curve

Normal Line to a Tangent

Slope of a Curve at a Point

Average Velocity

Instantaneous Velocity

Limit Definition of Derivative

First Principles Example 1: x²

First Principles Example 2: x³

First Principles Example 3: square root of x

Standard Notation and Terminology

Differentiable vs. Nondifferentiable Functions

Rate of Change of a Function

Average Rate of Change Over an Interval

Instantaneous Rate of Change at a Point