## owlet one year ago For the ffg. lines in $$R^2$$, determine a vector equation and parametric equations. $$\Large x_2 = 3x_1 + 2$$

1. owlet

@Luigi0210

2. owlet

@nincompoop

3. owlet

@mathmate

4. anonymous

introducing a parameter is easy -- take $$x_1=t$$, giving us the system; $$\left\{\begin{matrix}x_1=t&\\x_2=3t+2&\end{matrix}\right.$$ to get a vector equation, just use the above: $$r(t)=\langle x_1,x_2\rangle=\langle t,3t+2\rangle=t\langle 1,3\rangle +\langle0,2\rangle$$

5. owlet

where did you get (0,2)?

6. anonymous

owlet, vector components are additive, so $$\langle a,b\rangle+\langle c,d\rangle=\langle a+c,b+d\rangle$$ and also multiplicative so $$\langle kx,ky\rangle =k\langle x,y\rangle$$

7. anonymous

which means $$\langle t,3t+2\rangle=\langle t,3t\rangle+\langle 0,2\rangle=t\langle 1,3\rangle+\langle0,2\rangle$$

8. owlet

aah okay. thanks.