Question

he point p(5, −2) lies on the curve y = 2 4 − x . (a) if q is the point x, 2 4 − x , find the slope of the secant line pq (correct to six decimal places) for the following values of x. (i) 4.9 mpq =

Answer 1

To find the slope of the secant line PQ, use the slope formula with P(5, -2) and Q(x, 2^4 - x), calculating the y-coordinate of Q for x=4.9 and then applying the slope formula.

Step-by-step explanation:

Finding the Slope of the Secant Line PQ

To find the slope of the secant line PQ for a point Q defined as (x, 24 - x), we can use the slope formula. The point P is given as (5, -2) and for this case, the point Q has an x-coordinate of 4.9. The y-coordinate of Q can be calculated as 24 - 4.9.

The slope (mpq) formula is:
(y2 - y1) / (x2 - x1)

By plugging in the coordinates of P and Q into the formula, we can get the slope of the secant line PQ:

For x = 4.9, the slope mpq = (24 - 4.9) - (-2) / (4.9 - 5). After calculating, round the slope to six decimal places as requested.