# How do you find the slope of the secant lines of # f (x) = x^2 − x − 42# at (−5, −12), and (7, 0)?

Assuming that the word "lines" should be "line", it is exactly the same as the slope of the line through the points (−5, −12), and (7, 0).

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To find the slope of the secant line between two points on a function ( f(x) ), you use the formula:

[ \text{Slope} = \frac{f(x_2) - f(x_1)}{x_2 - x_1} ]

Given the points ((-5, -12)) and ((7, 0)), the coordinates are ( (x_1, f(x_1)) = (-5, -12) ) and ( (x_2, f(x_2)) = (7, 0) ), respectively.

Plug the values into the formula:

[ \text{Slope} = \frac{0 - (-12)}{7 - (-5)} ]

[ \text{Slope} = \frac{12}{12} ]

[ \text{Slope} = 1 ]

So, the slope of the secant line of ( f(x) = x^2 - x - 42 ) at the given points is ( 1 ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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