linear equations

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hbxdz

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Hi , is their any way to find the linear equation of a parametric equation ?
i don't know how im i supposed to do this , i only know when u have points :/ ?
thank you

(x,y,z) = (1,-1,1)+r(0,-3,-6)+s(2,0,-6)
 
Do you see that this equation can be written as a system of three linear equations in r and s (thinking of x, y, and z as constants)?

Eliminate r and s from the equations, and you will be left with a single equation in x, y, and z.
 
okay and how do i change it to ax+by=c ?

x=(1,-1,1)
y=(0,-3,-6)
z=(2,0,-6)
 
hbxdz said:
… how do i change it to ax+by=c ? …
Click to expand...
Hi hbxdz. That's not the correct form because the line in your exercise is in 3-dimensional space. The points have ordered triples for coordinates: (x,y,z).

The form ax + by = c denotes a line in the plane, where points have ordered pairs for coordinates: (x,y).

The answer for your exercise has this form:

ax + by + cz = d

Please show your work for eliminating the parameters, if you get stuck, so we can see what you've tried. Cheers

?
 
Ok so im here , i understand how to take off the X,y,z from the first equation ,
but after that i don't understand how im supposed to find a linear equation ?
Im i supposed to find out ''r'' and ''s'' if yes , i did it and it doesn't work !
 

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You have the equations

1 + 2s = x​
-1 - 3r = y​
1 - 6r - 6s = z​

Do the same thing you'd do to solve for r and s if x, y, and z were just numbers. You might, for example, solve the first equation for s, the second for r, and substitute those into the third.

The goal is not primarily to find r and s, but to eliminate them, so you get one equation that has only x, y, and z, not r or s.
 
okay i did it

the equation i got is : z=1-6((y+1)/-3)-6((x-1)/2)

so after that all i need to do is to replace it like ax+by+cz=d ?

and the x y and z ?


-
 
hbxdz said:
okay i did it

the equation i got is : z=1-6((y+1)/-3)-6((x-1)/2)

so after that all i need to do is to replace it like ax+by+cz=d ?

and the x y and z ?
Click to expand...
I wouldn't say "replace"; just simplify it to put it in the desired form. That may be what you meant.
 
Dr.Peterson said:
You seem to have lost the y and some constants!
Click to expand...
Thank you. Actually, I got burned by not checking a machine's result, after pasting the RHS into a simplify command (one of the implied multiplications didn't take).

I've deleted my post, and I'm heading for the corner.

?
 
And let's just add this- since this results in a single linear equation in the three variables, x, y, z, it is the equation of a plane, not a line!
 
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