Question 967413
Find the line which contains (0,0) and has slope {{{3/4}}}.
{{{y-0=(3/4)(x-0)}}}
{{{y=(3/4)x}}}
The general point (x,(3/4)x ).


You want to find the point on that line which is 2 units from (0,0).
{{{sqrt((x-0)^2+((3/4)x-0)^2)=2}}}
{{{sqrt(x^2+9x^2/4)}}}=2
{{{x*sqrt(1+9/4)=2}}}
{{{x*sqrt(13/4)=2}}}
{{{(x/2)sqrt(13)=2}}}
{{{x=4/sqrt(13)}}}
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Corresponding y value is (3/4)(4/sqrt(13))
{{{y=3/sqrt(13)}}}.


That will be part of one possible answer.


You are looking for a line  with that point just found with the equation member of {{{4x+3y}}} because you are looking for the line PARALLEL to the given line. 


{{{highlight(4x+3y=4((4/sqrt(13)))+3((3/sqrt(13))))}}}.
That needs to be simplified in order to be completely finished.