Find the slope of the secant line between the values $x_{1}$ and $x_{2}$ for the function given below.
$f (x) = \frac{4 x + 3}{5 x + 5}; x_{1} = 6, x_{2} = - 10$
The slope is
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Answer

Final Answer: The slope of the secant line between the values $x_{1}$ and $x_{2}$ for the function given is $- 0.0031746031746031703$

Steps

Step 1 ：Given the function $f (x) = \frac{4 x + 3}{5 x + 5}$ and the points $x_{1} = 6$ and $x_{2} = - 10$

Step 2 ：First, we need to find the values of $f (x_{1})$ and $f (x_{2})$

Step 3 ：Substitute $x_{1} = 6$ into the function to get $f (x_{1}) = 0.7714285714285715$

Step 4 ：Substitute $x_{2} = - 10$ into the function to get $f (x_{2}) = 0.8222222222222222$

Step 5 ：Then, we use the formula for the slope of the secant line: $m = \frac{f (x_{2}) - f (x_{1})}{x_{2} - x_{1}}$

Step 6 ：Substitute the values into the formula to get $m = - 0.0031746031746031703$

Step 7 ：Final Answer: The slope of the secant line between the values $x_{1}$ and $x_{2}$ for the function given is $- 0.0031746031746031703$