Question

The point P(1, 1/6) lies on the curve y = x/(5 + x). If Q is the point (x, x/(5 + 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.

Answer 1

The slope of the secant line PQ is 0.

Step-by-step explanation:

To find the slope of the secant line PQ, we need to determine the coordinates of Q and P. Given that Q has the coordinates (x, x/(5+x)), we can substitute x=1 into the equation to find Q. So, Q is (1, 1/6).

The slope of a line passing through two points can be found using the formula:

slope = (y2 - y1) / (x2 - x1)

Substituting the coordinates of P and Q into the formula:

m = (1/6 - 1/(5+1)) / (1 - 1) = (1/6 - 1/6)/(0) = 0

Therefore, the slope of the secant line PQ is 0.

Answer 2

`m(x)=(5)/(6(5+x))`

Step-by-step explanation:

Slope of the secant line PQ:

P : (1, 1/6)

Q : (x, x/(5 + x))

`m(x)=(y_(Q)-y_(P))/(x_(Q)-x_(P))=(x/(5 + x)-1/6)/(x-1)=(5(x-1))/(6(5+x)(x-1))`