How do you graph #x+3y=6# using intercepts?

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Answer 1 · 2017-01-21T13:41:04

Find the intercepts by setting #x=0# or #y=0# and solving, then draw a line through them...

Given:

#x+3y = 6#

we can find the intercepts by setting #x=0# or #y=0# and solving. This is equivalent to crossing out the term involving #x# or that involving #y#.

In any case, putting #x=0# we have:

#3y = 6#

and hence #y = 6/3=2#

So the intersection with the #y# axis (which has equation #x=0#) is at the point #(0, 2)#

Putting #y=0# we have:

#x = 6#

So the intersection with the #x# axis is at #(6, 0)#

Since there are no terms of degree #> 1#, the given equation describes a line through these two intercepts:

graph{(x+3y-6)(x^2+(y-2)^2-0.02)((x-6)^2+y^2-0.02) = 0 [-7.71, 12.29, -3.8, 6.2]}