How do you find the slope of the secant lines of $f (x) = (\frac{1}{x})$ $f(x) = (1/x)$ through the points: (-4,(f(-4)) and (1,f(1))?

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How do you find the slope of the secant lines of $f (x) = (\frac{1}{x})$ $f(x) = (1/x)$ through the points: (-4,(f(-4)) and (1,f(1))?

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Answer 1 · 2017-12-01T15:51:12

$\frac{1}{4}$ $1/4$

Explanation:

To find the slope is the same as finding the slope of any line i.e.:

$\frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ $(y_2-y_1)/(x_2-x_1)$

$\frac{f (- 4) - f (1)}{(- 4) - (1)} = \frac{(- \frac{1}{4}) - (1)}{- 5} = \frac{- \frac{5}{4}}{- 5} = \frac{1}{4}$ $(f(-4)-f(1))/((-4)-(1))=((-1/4)-(1))/(-5)=(-5/4)/(-5)=1/4$

The equation of the secant line is:

$y = \frac{1}{4} x + \frac{3}{4}$ $y=1/4x+3/4$

and you can see the gradient is $\frac{1}{4}$ $1/4$

Graph:

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How do you find the slope of the secant lines of $f (x) = (\frac{1}{x})$ $f(x) = (1/x)$ through the points: (-4,(f(-4)) and (1,f(1))?

1 Answer

Explanation:

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How do you find the slope of the secant lines of $f (x) = (\frac{1}{x})$ $f(x) = (1/x)$ through the points: (-4,(f(-4)) and (1,f(1))?