How do you graph #x+y=3#?

1 Answer
Geoff K.
May 21, 2018

Easiest way: plot #(0,3)# and #(3,0)# on a graph; connect them with a line.

Explanation:

We're looking for all pairs of numbers that add to 3.

There are infinitely many #(x,y)# pairs that work; we want to show where they are on an #x"-"y# plane.

Two pairs are easy to find. We know that #0 + 3=3# and we know #3+0=3#. That means the points #(0,3) and (3,0)# are both on our graph. We plot those points:

graph{(x^2+(y-3)^2)*((x-3)^2+y^2)=0.3 [-10, 10, -5, 5]}

It's not hard to find a couple more. For instance, #1+2=3# and #2+1=3#, so both #(1,2) and (2,1)# will be on our graph as well.

As you may be able to tell already, these points all fall in a straight line. That means the collection of all pairs #(x,y)# that satisfy #x+y=3# will be on this line:

graph{(x^2+(y-3)^2-0.04)*((x-3)^2+y^2-0.04)(x+y-3)=0 [-10, 10, -5, 5]}

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