Question

graph x+y+Z=6

Answer 1

So this is a 3D plane, isn't it?

Answer 2

yes

Answer 3

eek 3-d. vectors all over again

Answer 4

Remember that when x, y are 0 then z is 6, when x, z are 0 then y is 6 etc

Answer 5

So plot the points on the intercepts first.

Answer 6

it has to be a plane, so it shouldn't be hard to make out the shape from there.

Answer 7

how would this look

Answer 8

Also, it has a normal vector of <1, 1, 1> so it is perpendicular to that vector.

Answer 9

You need the little-known but very useful Intercept Form. Divide by 6.

x/6 + y/6 + z/6 = 1

This is the Intercept Form. It says:

x-intercept (6,0,0)
y-intercept (0,6,0)
z=intercept (0,0,6)