# Thread: Parametrizing a line segment

1. ## Parametrizing a line segment

I am given two points.
(-2,5) and (4,3)

I kind of understand the concept, but am not totally clear.
I know I use...

x= x + at
y= y + bt

I dont get where to put the x's and y's...and what to use for t. How do I know which is which when t = 0 or t = 1?

2. Hi Morgan82!

Originally Posted by Morgan82
I am given two points.
(-2,5) and (4,3)

I kind of understand the concept, but am not totally clear.
I know I use...

x= x + at
y= y + bt
No, thats not true.

point has the coordinates (t,y), then the equation is

y = a + t*x

There are two points (-2,5) and (4,3), this leads to

5 = a+(-2)x
e.g.

5 = a - 2x (eq 1)

3 = a + 4*x (eq 2)

and now you need to solve the equations, like this

(eq1) - (eq2)

5-3 = a -2x - (a +4x)

2 = a -2x - a - 4x

2 = -6x

x = -1/3

Now you know x and substitute it in eq 1 (substitute in eq 2 would work, too)

5 = a - 2*(-1/3) (x=-1/3 in eq 1)

5 = a + 2/3

5 - 2/3 = 13/3 = a

So the solution is y = 13/3 -1/3*x

Do you understand?

Yours
Rapha

Originally Posted by Morgan82
I dont get where to put the x's and y's...and what to use for t. How do I know which is which when t = 0 or t = 1?