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Answer 1 · 2017-10-30T08:20:50

#x=-1+3lambda#

#y=6-9lambda#

the vector eqn of a straight line in vector form is:

#vecr=veca+lambdavecd#

we shall write the vectors in column form so that the parametric eqns can be spotted easily

where

#vecr=((x),(y))" "#is the general point on the line

#veca=#a known position vector on the line

#vecd=#the direction of the line

in this question

#veca=((-1),(6))#

the line is parallel to# <3,-9>#

#:.vecd=((3),(-9))#

#:.vecr=((-1),(6))+lambda((3),(-9))#

#((x),(y))=((-1),(6))+lambda((3),(-9))#

#=>x=-1+3lambda#

#y=6-9lambda#

which are the parametric eqns