Question

The point P(7, −3) lies on the curve y = 3/(6 − x). (a) If Q is the point (x, 3/(6 − x)), use your calculator to find the slope mPQ of the secant line PQ (correct to six decimal places) for the following values of x. (i) 6.9 mPQ = 1

Answer 1

Answer:

The right answer is "3.33333".

Step-by-step explanation:

The given points in the question are:

$P=(7,-3) = (x_1,y_1)$

$Q=(x,\frac{3}{6-x} )=(x_2,y_2)$

Now,

The slope of PQ will be:

= $\frac{y_2-y_1}{x_2-x_1}$

By putting the values, we get

= $\frac{\frac{3}{6-x}+3 }{x-7}$

= $\frac{3+18-3x}{(6-x)(x-7)}$

= $\frac{21-3x}{(6-x)(x-7)}$

= $\frac{3(x-7)}{(6-x)(x-7)}$

= $\frac{3}{x-6}$

hence,

x = 6.9

it's slope will be:

= $3.33333$