Question

Write one parametric equation that represents the same line in different ways.
How are you supposed to reason? I don't really get parametric functions.

Answer 1

is this a 2d line we're talking about?

Answer 2

Yes, I believe so.

Answer 3

It's something about vector coordinates written on the form y=kx+m and then transformed into "parametric" equations. I hate my book. :(

Answer 4

ok vectors :D try and explain what i think they mean

Answer 5

lets take for example y =5x + 2

Answer 6

this has a gradient of 5 and a y intercept of 2

this is the "Cartesian" equation of that line

Answer 7

with vectors the way i always think about them is a set of instructions, for example here we want to know how to get from (0,0) to any point on that line

Answer 8

<0,0> being the position vector O?

Answer 9

yes

Answer 10

now we choose a single point on the line and get the position vector of that point

Answer 11

so choose a point on y = 5x +2 for me

Answer 12

any point

Answer 13

(a,b)

Answer 14

haha nice, a general point, although i prefer your choice im going to use a concrete example just for this first line ok?
(0,2) is on our line
ok so that has position vector

\[\left(\begin{matrix}0 \\ 2\end{matrix}\right)\]

this is our starting point, our vector equation will go to there first.

now we need a "direction vector"

we need a vector parallel to our line

lets call \[A = \left(\begin{matrix}0 \\ 2\end{matrix}\right)\]
if we now take another point on the line B, and find the vector AB

that will be parallel to our line we are trying to define

Answer 15

sorry, where i put "A" i meant "OA"
lets use
\[OB = \left(\begin{matrix}1 \\ 7\end{matrix}\right)\]

the vector AB is equal to OB - OA