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For the function
f(x)=x^(2)-2, find the slope of the secant line between
x=-5 and
x=-2.
Answer:

For the function $f(x)=x^{2}-2$ , find the slope of the secant line between $x=-5$ and $x=-2$ . $\newline$ Answer:

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Write a linear equation from two points

Full solution

Q. For the function

f(x)=x^{2}-2

, find the slope of the secant line between

x=-5

and

x=-2

.

\newline

Answer:

Calculate $f(-5)$ : Calculate the value of the function $f(x)$ at $x = -5$ .
$f(-5) = (-5)^2 - 2$
$f(-5) = 25 - 2$
$f(-5) = 23$
Calculate $f(-2)$ : Calculate the value of the function $f(x)$ at $x = -2$ .
$f(-2) = (-2)^2 - 2$
$f(-2) = 4 - 2$
$f(-2) = 2$
Find slope of secant line: Use the values of $f(-5)$ and $f(-2)$ to find the slope of the secant line. $\newline$ The slope of the secant line ( $m$ ) is given by the difference in the y-values divided by the difference in the x-values. $\newline$ $m = \frac{f(-2) - f(-5)}{-2 - (-5)}$ $\newline$ $m = \frac{2 - 23}{-2 + 5}$ $\newline$ $m = \frac{-21}{3}$ $\newline$ $m = -7$

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