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))?

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Answer 1 · 2017-12-01T15:51:12

#1/4#

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

#(y_2-y_1)/(x_2-x_1)#

#(f(-4)-f(1))/((-4)-(1))=((-1/4)-(1))/(-5)=(-5/4)/(-5)=1/4#

The equation of the secant line is:

#y=1/4x+3/4#

and you can see the gradient is #1/4#

Graph:

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