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]}

Related questions
See all questions in Graphs in the Coordinate Plane
Impact of this question
14530 views around the world
You can reuse this answer
Creative Commons License