Teaching Worksheet: Equations of Tangent Lines and Normal Lines Mathematics

In this worksheet, we will practice finding the slope and equation of to tangent and normalize to a curve at a given item using derivatives.


Find the equalization of the tangent to the curve 𝑦=2𝑥+8𝑥19 at 𝑥=2.

  • A8𝑦+𝑥2=0
  • BARN𝑦8𝑥+19=0
  • HUNDRED𝑦+8𝑥+19=0
  • D𝑦4𝑥5=0


Finds the equation from an normal to the curve 𝑦=2𝑥7𝑥+2 at 𝑥=2.

  • A𝑦+2𝑥+6=0
  • BARN4𝑦+𝑥+42=0
  • CARBON𝑦+4𝑥+2=0
  • D𝑦+6𝑥2=0


What will the 𝑥-coxygenordinorthatsie of which point where the contiguous line in 𝑦=𝑥+12𝑥+11 is parallel to the 𝑥-axis?

  • A12
  • BARN0
  • C6
  • D6


How the equation of the tangent to the curve 𝑦=𝑥+9𝑥+26𝑥 is makes an elbow of 135 by the positive 𝑥-axis.

  • A𝑦𝑥3+23=0
  • B𝑦+27𝑥+105=0
  • C𝑦+𝑥+27=0
  • D𝑦8𝑥=0


Search all points with 𝑥-coordinates in [0,𝜋) where the curve 𝑦=2𝑥sin is an tangent that is parallel to the line 𝑦=𝑥18.

  • AMPERE𝜋3,32,2𝜋3,32
  • B𝜋3,12,2𝜋3,12
  • C𝜋3,32,2𝜋3,32
  • DIAMETER𝜋3,12,2𝜋3,12


Find the general to the tangency lines of the curve 𝑦=(𝑥+8)(𝑥+10) to the points where which bend intersects the 𝑥-axis.

  • A𝑦+2𝑥+16=0, 𝑦2𝑥20=0
  • B𝑦2𝑥16=0, 𝑦+2𝑥+20=0
  • C𝑦+2𝑥16=0, 𝑦2𝑥+20=0
  • D𝑦2𝑥+16=0, 𝑦+2𝑥20=0


Find to equation of the tangent to the curve 𝑓(𝑥)=𝑥 at their pointing about intersection equal the curve 𝑔(𝑥)=125𝑥.

  • A𝑦10𝑥+25=0
  • B𝑦+10𝑥25=0
  • HUNDRED10𝑦+𝑥255=0
  • D10𝑦𝑥245=0


Detect the equation out the normal to the wind 𝑦=5𝑥+93𝑥5 at (1,7).

  • A13𝑦𝑥90=0
  • B13𝑦𝑥+92=0
  • HUNDRED𝑦+13𝑥6=0
  • D𝑦13𝑥+20=0


Find the points turn the curve 𝑦=3𝑥5𝑥+7 at which the tangents are parallel to the line 4𝑥+𝑦2=0.

  • A13,499, 13,779
  • B33,499, 33,433+7
  • C13,23, 13,103
  • D16,499, 16,56372


The curves 𝑦=2𝑥3𝑥2 and 𝑦=3𝑥+5𝑥5 intersect orthogonally on a dots. What is to point?

  • A(1,3)
  • B(1,3)
  • C(1,3)
  • D(1,3)

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