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Let f ( x ) = x 2 − 2 x f ( x ) = x 2 - 2 x . Round all answers to 2 decimal places. a . a . Find the slope of the secant line joining ( 2 , f ( 2 ) ( 2 , f ( 2 ) and ( 8 , f ( 8 ) ) ( 8 , f ( 8 ) ) .

User Tonfa
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1 Answer

4 votes

Answer:

The slope of the secant line joining (2, 0) and (8, 48) is 8.

Explanation:

Let
f(x) = x^(2)-2\cdot x, from Analytical Geometry we remember that slope of a secant line is defined by:


m_(sec) = (f(x_(B))-f(x_(A)))/(x_(B)-x_(A)) (Eq. 1)

Where:


x_(A),
x_(B) - Initial and final independent variables, dimensionless.


f(x_(A)),
f(x_(B)) - Initial and final dependent variables, dimensionless.

Now we proceed to find the values of each dependent variable:


x_(A) = 2


f(x_(A)) = 2^(2)-2\cdot (2)


f(x_(A)) = 0


x_(B) = 8


f(x_(B)) = 8^(2)-2\cdot (8)


f(x_(B)) = 48

And slope of the secant slope is determined after replacing every variable:


m_(sec) = (48-0)/(8-2)


m_(sec) = 8

The slope of the secant line joining (2, 0) and (8, 48) is 8.

User Kamek
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