How do you find the equation of the line tangent to the graph of y=x2−3...

Leroy Little

Leroy Little

Answered question

2022-02-12

How do you find the equation of the line tangent to the graph of y=x23 at the point P(2,1)?

Answer & Explanation

Addison Matthews

Addison Matthews

Beginner2022-02-13Added 13 answers

Explanation:
The slope of a tangent to y=x23 is given by its derivative:
m=dydx=2x
At (x,y)=(2,1) the slope becomes (substituting 2 for x) m=4
The general slope point form for a line with slope m through a point (x^,y^) is yy^=m(xx^)
Substituting m=4, x^=2, and y^=1
y-1=4(x-2)
This could be re-written in standard form as
4x-y=7

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