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For the function
f(x)=x^(2)+5x-9, find the slope of the secant line between
x=-7 and
x=4.
Answer:

For the function $f(x)=x^{2}+5 x-9$ , find the slope of the secant line between $x=-7$ and $x=4$ . $\newline$ Answer:

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Complex conjugate theorem

Full solution

Q. For the function

f(x)=x^{2}+5 x-9

, find the slope of the secant line between

x=-7

and

x=4

.

\newline

Answer:

Slope Formula: To find the slope of the secant line between two points on a function, we use the formula for slope, which is the change in $y$ -values divided by the change in $x$ -values. This is also known as the difference quotient and is given by $\frac{f(x_2) - f(x_1)}{x_2 - x_1}$ , where $x_1$ and $x_2$ are the $x$ -values of the two points.
Find $f(-7)$ : First, we need to find the y-value when $x = -7$ by substituting $-7$ into the function $f(x)$ . So, $f(-7) = (-7)^2 + 5(-7) - 9$ .
Calculate $f(-7)$ : Calculating $f(-7)$ gives us $f(-7) = 49 - 35 - 9 = 5$ .
Find $f(4)$ : Next, we need to find the y-value when $x = 4$ by substituting $4$ into the function $f(x)$ . So, $f(4) = (4)^2 + 5(4) - 9$ .
Calculate $f(4)$ : Calculating $f(4)$ gives us $f(4) = 16 + 20 - 9 = 27$ .
Identify Two Points: Now we have the two points on the function: $(-7, 5)$ and $(4, 27)$ . We can use these to find the slope of the secant line.
Calculate Slope: The slope of the secant line is $(f(4) - f(-7)) / (4 - (-7)) = (27 - 5) / (4 + 7)$ .
Final Result: Calculating the slope gives us $(22) / (11) = 2$ .

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