Question 982936
The line has slope 2 and y-intercept is given.  The line has the equation {{{y=2x+2}}}.


The intersection points A and B will be for {{{1/x=2x+2}}} formed by equating the two expressions for y.  This will be a quadratic equation giving two x coordinates.


{{{2x+2=1/x}}}
{{{2x^2+2x=1}}}
{{{2x^2+2x-1=0}}}


Discriminant is  {{{2^2-4*2*(-1)=4+8=12}}}.
{{{x=(-2+- sqrt(12))/4}}}

{{{x=(-2+- 2*sqrt(3))/4}}}

{{{x=(-1+- sqrt(3))/2}}}


---
The two points to be found,  still unfinished, would be as these:


{{{x=(-1-sqrt(3))/2}}}  and  {{{y=2/(-1-sqrt(3))}}}
-
{{{x=(-1+sqrt(3))/2}}}  and  {{{y=2/(-1+sqrt(3))}}}.



{{{graph(300,300,-4,4,-4,4,1/x,2x+2)}}}