Secant and Tangent Lines

Secant and tangent line

​In today's lesson:

1. ​Quick quiz

2. ​Fun cards

3. ​What is a secant line? Tangent line?

4. More math

5. Test yourself

Multiple Choice

What does "tangent" mean?

• Ice cream in Italian

• Rope in Greek

• Touching in Latin

• Departure in Egyptian

Multiple Choice

What does "secant" mean in Latin?

• To cut

• To sew

• To cross

• To nap

​Cards

​Access this link: https://student.desmos.com/join/76dbr3

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​Work in pairs to sort the cards on desmos.

​What is a secant line?

A secant line is ​a line that intersects a curve at a minimum of two points.

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What is a tangent line? ​

​It is a line that is tangent to a curve meaning that it touches the curve at a single point and then continues un either direction with exactly the slope of the curve at that point.

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​"Going off on a tangent"

Tangent line rule #1

Tangent line must touch the curve.

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The line that is most similar to the curve at the point

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​https://www.geogebra.org/m/s4pzuuzu

Tangent line rule #2

​Limit from the left = limit from the right

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https://www.geogebra.org/calculator/axhkkkwv

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​CAREFUL!!!!!!!

​This is a counter example:

​https://www.geogebra.org/calculator/axhkkkwv

Back to your cards

​Take a look at your cards and make

some changes based on the info

that we discussed.

​How to find the equation of the tangent line?

​1. By knowing the coordinates of two points on the tangent line.

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​Example:

​A(1,1) and B(2,3)

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​y-y₁=m(x-x₁)

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​How to find the equation of the tangent line?

​2. Using derivatives

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​Secant line:

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​Tangent line:

​

​

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https://www.geogebra.org/calculator/axhkkkwv

​Test yourself aka homework

​Try to solve these exercises by yourself!

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​Find the equations of the tangent lines going through A and B using two different ways.

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A(-1,1) and B(1,3)

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​The tangent lines intersect at a point C(0.5,-0.5)

​Have a nice day!