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The function f(x) has the property that if P and Q are any two distinct points on the graph of y = f (x), then the slope of PQ is equal to 1.  What is the value of f(10) - f(0)?

\(\phantom{twice the sum of the x-coordinates of P and Q.}\)

 Jul 9, 2022
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Make sure you credit where the original problem came from! This, I believe, is from MATHCOUNTS States.

In the graph of y = f(x), we know that two coordinates are:

 

(10, f(10))

(0, f(0)).

 

Finding the slope of these two points gives us:

(f(10)-f(0))/10 = 1

Therefore, f(10)-f(0) = 10. 

 Jul 10, 2022

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