Question

The point P(8, −3) lies on the curve y = 3/(7 − x). (a) If Q is the point (x, 3/(7 − 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) 7.9 mPQ =

Answer 1

Answer:

Slope of the line $PQ is -63.434948.$

Step-by-step explanation:

Given that,

The point $P(8,-3)$ lies on the curve $y=\frac{3}{7-x}$.

If $Q$ is the point lies on $(x,\frac{3}{7-x} )$.

To find:- Find the slope of line $PQ$.

So,  

The coordinates of point $Q$ when it lies on $(x,\frac{3}{7-x} )$

        if $x=1$ then $y= \frac{3}{7-1} =\frac{3}{6} =\frac{1}{2}$

       So,   $Q$ ≡ $(1,\frac{1}{2} )$ and many points can be calculated by given Equation.

Using the formula when two points $(x_{1} ,y_{1} ) \& (x_{2}, y_{2} )$.

                $Slope=Tan\theta = \frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

Then, substituting the coordinates we get,

             $Slope = \frac{1-8}{\frac{1}{2}-(-3) }$

             $Slope = \frac{-7}{\frac{1}{2}+3 } = \frac{-7}{\frac{7}{2} }$

             $Slope = \frac{-14}{7}=-2$

              $tan\theta=-2$   ⇒  $\theta = tan^{-1} (-2)$

               $\theta= -63.434948$

Therefore,

Slope of the line $mPQ is -63.434948.$