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Question 503827: write a linear equation in three dimension with the following intercerpts:
x intercept is 25, y intercept is 50 and z intercept is 10
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! ax + by + cz + d = 0
that's the standard form of a linear equation in 3 dimensions.
a is the coefficient of the x term
b is the coefficient of the y term
c is the coefficient of the z term
d is the constant.
if we move the constant over to the right side of the equation, then we get:
ax + by + cz = -d
to find the x intercept, we set y and z equal to 0.
we get:
ax = -d
this makes x = -d/a
similarly, to find the y intercept we set x and z equal to 0.
we get:
by = -d
similarly, to find the z intercept, we set x and y equal to 0.
we get:
cz = -d
we can set d equal to anything we want.
then all we have to do is solve for a, b, and c.
suppose we set d to be equal to -100.
then -d = 100.
we get:
ax = 100 when y and z are equal to 0.
by = 100 when x and z are equal to 0.
cz = 100 when x and y are equal to 0.
let's start with ax = 100
we want x to be equal to 25 when y and z are equal to 0.
ax = 100 becomes 25a = 100 when x is replaced with 25.
this makes a equal to 100/25 = 4
next we'll work with bx = 100
we want y to be equal to 50 when x and z are equal to 0.
by = 100 becomes 50b = 100 when y is replaced with 50.
this makes b equal to 100/50 = 2.
next we'll work with cz = 10
we want z to be equal to 10 when x and y are equal to 0.
cz = 100 becomes 10z = 100 when z is replaced with 10.
this makes c = 100/10 = 10
we have:
a = 4
b = 2
c = 10
d = -100
our equation becomes:
4x + 2y + 10z = 100
when y and z are equal to 0, we get 4x = 100 which makes x = 25
when x and z are equal to 0, we get 2y = 100 which makes y = 50
when x and y are equal to 0, we get 10z = 100 which makes z = 10
the requirements of the problem are satisfied, so we're good.
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