Question 322079
A line is given by : set of (x,y)=OP+a*(dx,dy)

OP is a point of the line, (dx,dy) is the vector giving the direction of the line.

we need 2 points of the line : e.g. OP=(0,-5/3) and OP1=(1,4/3)

hence : (dx,dy)=(1,3)

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For the seeked line we put OP2=(1,-2) and the same vector of direction, to be parallel : 

line 2 is the set of :(x2,y2)=(1,-2)+a(1,3)

x2=1+a
y2=-2+3a

eliminate a : 3x2-y2=5

hence : equation is : 9x-3y=15 (which is just first equation, with the RHS 
obtained by putting (x,y)=(1,-2) : 9-3*(-2)=15)