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Am I right in saying:

ax+b=0 is one-variable linear equation

ax+by+c=0 is two-variable linear equation

ax^2+bx+c=0 is one-variable quadratic equation

ax^2+bx+c=y is two-variable quadratic equation

Every linear or quadratic equation in one or two variables can be represented in those ways.

How come graph of ax+by+c=0 is point of solution set {(x,y) | ax+by+c=0}? Why not (y,x)? Since we can rearrange it as x=(y=b)/m, can we pick the y value first and then find the x value?

I know graph of x=a and y=a is vertical and horizontal lines respectively because x or y will always be constant no matter what y or x is respectively. But how would we represent the solution sets? For x=a, would it be {(x,y) | x+0y=a}?

Thanks.

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# Ax+b=0 is one-variable linear equation

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