Question

the 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 with points P(5, -2) and Q(x, 24 - x), substitute the x-coordinate of Q into the curve equation to find the y-coordinate. Then use the slope formula to calculate the slope of PQ.

Step-by-step explanation:

The slope of a curve at a point is equal to the slope of a straight line tangent to the curve at that point. To find the slope of the secant line PQ, we need to calculate the slope between points P and Q. Since P(5, -2) and Q(x, 24 - x), we can substitute the x-coordinate of Q into the equation for the curve to find the y-coordinate. For x = 4.9, the y-coordinate of Q would be 24 - 4.9 = 19.1. Then, we can use the formula for slope to find the slope of PQ: m = (y2 - y1) / (x2 - x1) = (19.1 - (-2)) / (4.9 - 5) = 21.1 / (-0.1) = -211.