Question

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

Answer 1

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]}