Question

Which line is the same as [x, y]=[1, -8] + t[ 4,-3]?
A [x, y] =[2, 4] +t[-4, 3]
B [x, y] =[13, 17]+t[8, -6]

Answer 1

And how do you figure it out?

Answer 2

you could just determine the line equation y(x), through substitution

Answer 3

@completeidiot how ?

Answer 4

[x, y]=[1, -8] + t[ 4,-3]

x=1+4t
y=-8-3t

solve for t for one of the equations, then substitute

Answer 5

by elimination ? @completeidiot

Answer 6

look for the coefficients of parallel vector.
if they are same means either same line or parallel

Answer 7

@sami-21 what do you mean ?

Answer 8

look the coefficients of parameter t .
each line in space has parallel vector to describe it . so if the vectors are same then lts same .

Answer 9

in other words i am saying compare following
x=1+4t
y=-8-3t

with A
x=2-4t
y=4+3t

and B
x=13+8t
y=17-6t

Answer 10

did you get it ?

Answer 11

im trying to understand it :S

Answer 12

well, let me show you how B is same as the given line.
each line in the space requires one point and vector to completely define it

the coefficients of the t represents that vector
so if the coefficients of the t are same or scalar multiple of some number then lines are definitely same .

so the vector parallel to given line is (coefficients of t )

v1=<4,-3>

vector paralel to line A (coefficients of t )
vA=<-4,3>

vector parallel to line B (coefficients of t )
vB=<8,-6>

you can see that

the vetor Vb parallel to line B is 2 times the vector parallel to given line
vB=2v1

it means given line and line |B are identical.
Hope its clear now .

Answer 13

Like how do i compare the parametric equations of A and B. Is there something i sub in ?

Answer 14

no i meant solve for t...

x=1+4t
x-1=4t

t=(x-1)/4

y=-8-3t

y=-8-3((x-1)/4)