Slope of a secant line

Question

Function	(a, f(a))
f(x) =  1 x	(1, 1)

(a) Use

f(a + h) − f(a)

h

 to find the slope of the secant line passing through the points (a, f(a)) and

(a + h, f(a + h)).

 

Answer 1

Let there be two points P1(x1,y1) and P2(x2,y2)

The slope of the line between P1 and P2 is,

m = Δy/Δx, where Δy = y2 – y1 and Δx = x2 – x1

Using the points given in the question we have P1(x1,y1) = (a, f(a)) and P2(x2,y2) = (a+h, f(a+h))

Then,

m = Δy/Δx = (y2 – y1)/(x2 – x1)

where (y2 – y1) = f(a+h) - f(a), and (x2 – x1) = (a+h) – h = h

Therefore, the slope of the secant line is: Δy/Δx = [f(a+h) - f(a)]/h