The point P(14,16)\displaystyle {P}{\left(\frac{{1}}{{4}},{16}\right)} lies on the curve y=4x\displaystyle {y}=\frac{{4}}{{x}}. If Q\displaystyle {Q} is the point (x,4x)\displaystyle {\left({x},\frac{{4}}{{x}}\right)}, find the slope of the secant line PQ\displaystyle {P}{Q} for the following values of x\displaystyle {x}.

If x=0.35\displaystyle {x}={0.35}, the slope of PQ\displaystyle {P}{Q} is:  

and if x=0.26\displaystyle {x}={0.26}, the slope of PQ\displaystyle {P}{Q} is:  

and if x=0.15\displaystyle {x}={0.15}, the slope of PQ\displaystyle {P}{Q} is:  

and if x=0.24\displaystyle {x}={0.24}, the slope of PQ\displaystyle {P}{Q} is:  

Based on the above results, guess the slope of the tangent line to the curve at P(0.25,16)\displaystyle {P}{\left({0.25},{16}\right)}.