Question

Find the equation of the plane which passes through O and is parallel to x-5y+z=7

Answer 1

x=−z+5y+7

Answer 2

hopefully this helped you out

Answer 3

parallel things differ by a constant ..

Answer 4

"solving" for x does not produce a different parallel equation of a plane :/

Answer 5

so how do you solve it?

Answer 6

at best: take the point the give you .. the origin; and apply the normal parts from the plane that they gave you to it

Answer 7

or, ignore the constant in the stated plane, and plug in the point to solve for the constant of the parallel plane

Answer 8

x-5y+z=7

x-5y+z=k

0-5(0)+0=k

0 = k

therefore: x-5y+z=0

Answer 9

so u substitue the 0 to the variables to solve for the plane?

Answer 10

more like to solve for the constant number, and that would give out the parallel plane?

Answer 11

parallel planes have the same basic parts ....

just like parallel lines have the same basic parts ...

they differ by a constant; that constant is what moves them up to down

Answer 12

alright, Thanks

Answer 13

given a normal (a,b,c) and a point (xo,yo,zo) we define a plane as:

a(x-xo)+b(y-yo)+c(z-zo) = 0

ax-axo+by-byo+cz-czo = 0

ax +by + cz - (axo+byo+czo) = 0
^^^^^^^^^^
the constant

parallel planes have the same abc parts, and the same generaic xyz parts; they differ only by the point used - which only alters the constant