Question

The point P(9, −2) lies on the curve

y = 2/(8 − x).
If Q is the point (x, 2/(8 − x)),find the slope PQ 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 find the coordinates of point Q, which is represented as (x, 2/(8-x)). Substituting the x-coordinate of point P, we get (9, 2/(8-9)). Simplifying this expression, we get (9, -2).

Now, we can find the slope of the secant line PQ using the slope formula: slope = (y2 - y1) / (x2 - x1). Substituting the coordinates of points P and Q, the slope becomes (-2 - (-2)) / (9 - x). Simplifying this expression, the slope of PQ is 0.

To find the average velocity of a position function over a time interval is essentially the same as finding the slope of a secant line to a function. Furthermore, to find the slope of a tangent line at a point a , we let the x -values approach a in the slope of the secant line.

When two secants intersect outside a circle, the circle divides the secants into segments that are proportional with each other. Two Secants Segments Theorem: If two secants are drawn from a common point outside a circle and the segments are labeled as below, then a ( a + b ) = c ( c + d ).