How do you find the slope of the secant lines of #f (x) = x ^2 - 4x + 5 # at (1, 2) and (5, 10)?

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Answer 1 · 2018-05-13T16:29:49

Slope of secant is #2#.

First let us confirm, whether #(1,2)# and #(5,10)# lies on #f(x)=x^2-4x+5#.

As #1^2-4*1+5=1-4+5=2#, #(1,2)# lies on the curve

and as #5^2-4*5+5=25-20+5=10#, #(5,10)# lies on the curve.

Now slope of line joining #(x_1,y_1)# and #(x_2,y_2)# is

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

and hence slope of secant is #(10-2)/(5-1)=8/4=2#

graph{(x^2-4x+5-y)((x-1)^2+(y-2)^2-0.01)((x-5)^2+(y-10)^2-0.01)(y-2x)=0 [-7.13, 12.87, 0.92, 10.92]}