The point P(1, 1/9) lies on the curve y = x/(8 + x). If Q is the point (x, x/(8 + x)), use a scientific calculator to find the slope of the secant line PQ

Question

The point P(1, 1/9) lies on the curve y = x/(8 + x). If Q is the point (x, x/(8 + x)), use a scientific calculator to find the slope of the secant line PQ (correct to six decimal places) for the following values of x.

(a) 0.5

(b) 0.9

(c) 0.99

(d) 0.999

(e) 1.5

(f) 1.1

(g) 1.01

(h) 1.001

Answer 1

You can set this up quite easily on Desmos by defining f(x) = x/(x+8).

Then add a table to Desmos with column headings x₁ and f(x₁).

Under the heading x₁, enter the x coordinates of Q.

Finally add another column to the table that looks like this (the slope of secant PQ).

[f(x₁) - 1/9] / (x₁ - 1) where (1, 1/9) represent the coordinates of point P.

Check it out:

desmos.com/calculator/xfec5ooly4