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

Dec 1, 2017

$\frac{1}{4}$

#### Explanation:

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

$\frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

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

The equation of the secant line is:

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

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

Graph: