Analitic geometry problem

[Learningforcomp]

Hello.
can you help me get ot the solution to this problem?
Find the value of a to witch the lines r:(x,y)=(-4,1)+k(1,2) ans S:2x+ay=3 are parallel
answer:-1


To find out if two lines are parallel I need to verify if the angular coeficients are the same but how can I do that with the vectorial formula of the line?(the r: one)
Your time and attention are deeply appreciated .
thank you.

[red12dog34]

The equation of the line r can be written as
[tex]\begin{cases} x = -4+k \\ y=1+2k \end{cases}[/tex]
or [tex]2x-y+9=0[/tex]
Two straight lines [tex]d_1:a_1x+b_1y+c_1=0, \ d_2:a_2x+b_2y+c_2=0[/tex] are parallel if and only if [tex]\displaystyle\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne\frac{c_1}{c_2}[/tex]
Then [tex]\displaystyle\frac{2}{2}=\frac{-1}{a}\ne\frac{9}{-3}\Rightarrow a=-1[/tex]