Vectors: Find the equation y-mx+b for L?

[Leandra509]

Hi everyone,

Let L be the line defined by the vector equation v⃗ =[−4−5]+t[−5−6]. Find the equation y=mx+b for L?

I'm really having trouble understanding how to do this so an explanation would be appreciated. Thanks!

 

[HallsofIvy]

Hi everyone,

Let L be the line defined by the vector equation v⃗ =[−4−5]+t[−5−6]. Find the equation y=mx+b for L?

I'm really having trouble understanding how to do this so an explanation would be appreciated. Thanks!

Uhh, -4-5= -9 and -5-6= -11 but I don't think that is what you mean. You mean the vectors [-4, -5] and [-5, -6], right?

When t= 0, the vector gives the point [-4, -5] and when t= 1, [-9, -11]. To find an equation, y= mx+ b, let x= -4, y= -5 to get -5= -4m+ b and let x= -9, y= -11 to get -11= -9m+ b. Solve those two equations for m and b.

 

[Ishuda]

Hi everyone,

Let L be the line defined by the vector equation v⃗ =[−4−5]+t[−5−6]. Find the equation y=mx+b for L?

I'm really having trouble understanding how to do this so an explanation would be appreciated. Thanks!

Another way to approach it:
Let v = [x, y] so that
x = -4 - 5 t
y = -5 - 6 t
then, from the x equation,
-5 t = x + 4 ==> t = - (x + 4) / 5.
Now use the y equation above to write y in terms of x, simplify and collect terms to determine m and b.