Graphing With Curves

So, everyone knows that if you draw an x-y axis and put two points on it, you can make a line, therefore, making a line graph. But how surprised was I yesterday, when I was doing my math as normal, solving simultaneous equations and determining whether they were inconsistent or equivalent, when I come upon a most curious thing, a curve graph.




Now, I had never encountered one of these before, but it turns out that, say you have an equation: 3x + 7y = 21. To graph this as a line you would just find the the x and y intercepts (7,3) and then draw a line between those points and extend it. But, turns out, if you square x and y, the graph will become a curve. So, change it to: 3x^2 + 7y^2 = 21. The graph of that is a curve.