Respuesta :
Answer:
Slope of the line [tex]PQ is -63.434948.[/tex]
Step-by-step explanation:
Given that,
The point [tex]P(8,-3)[/tex] lies on the curve [tex]y=\frac{3}{7-x}[/tex].
If [tex]Q[/tex] is the point lies on [tex](x,\frac{3}{7-x} )[/tex].
To find:- Find the slope of line [tex]PQ[/tex].
So,
The coordinates of point [tex]Q[/tex] when it lies on [tex](x,\frac{3}{7-x} )[/tex]
if [tex]x=1[/tex] then [tex]y= \frac{3}{7-1} =\frac{3}{6} =\frac{1}{2}[/tex]
So, [tex]Q[/tex] ≡ [tex](1,\frac{1}{2} )[/tex] and many points can be calculated by given Equation.
Using the formula when two points [tex](x_{1} ,y_{1} ) \& (x_{2}, y_{2} )[/tex].
[tex]Slope=Tan\theta = \frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
Then, substituting the coordinates we get,
[tex]Slope = \frac{1-8}{\frac{1}{2}-(-3) }[/tex]
[tex]Slope = \frac{-7}{\frac{1}{2}+3 } = \frac{-7}{\frac{7}{2} }[/tex]
[tex]Slope = \frac{-14}{7}=-2[/tex]
[tex]tan\theta=-2[/tex] ⇒ [tex]\theta = tan^{-1} (-2)[/tex]
[tex]\theta= -63.434948[/tex]
Therefore,
Slope of the line [tex]mPQ is -63.434948.[/tex]
