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For the function
f(x)=x^(2)-7, find the slope of the secant line between
x=-6 and
x=-4.
Answer:

For the function $f(x)=x^{2}-7$ , find the slope of the secant line between $x=-6$ and $x=-4$ . $\newline$ Answer:

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Find the slope of a tangent line using limits

Full solution

Q. For the function

f(x)=x^{2}-7

, find the slope of the secant line between

x=-6

and

x=-4

.

\newline

Answer:

Calculate Y-Values: 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 $y$ divided by the change in $x$ (rise over run). This is given by the formula $(f(x_2) - f(x_1)) / (x_2 - x_1)$ , where $x_1$ and $x_2$ are the $x$ -values of the two points.
Find Two Points: First, we need to find the y-values for the points where $x = -6$ and $x = -4$ by plugging these x-values into the function $f(x) = x^2 - 7$ . For $x = -6$ : $f(-6) = (-6)^2 - 7 = 36 - 7 = 29$ . For $x = -4$ : $f(-4) = (-4)^2 - 7 = 16 - 7 = 9$ .
Calculate Slope: Now we have two points: $(-6, 29)$ and $(-4, 9)$ . We can use these points to find the slope of the secant line. $\newline$ Slope = $(f(-4) - f(-6)) / (-4 - (-6)) = (9 - 29) / (-4 + 6) = (-20) / 2 = -10$ .
Final Result: The slope of the secant line between $x = -6$ and $x = -4$ for the function $f(x) = x^2 - 7$ is $-10$ .

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