Can a mathematician tell me why slope is written y=mx+b instead of (x,mx+b) idk why but showing the equation as a point on the graoh makes sense tk me
First, "slope" isn't written as y=mx+b, that's the equation of a line, and in that equation, m is the slope. But I think probably you knew this and just typed the wrong thing. So, moving on.
Writing (x,mx+b) isn't really wrong. I can say "the line is the set of all points (x,y) that satisfy the equation y=mx+b" or "the line is the set of all points of the form (x, mx+b)" and these are both valid ways to talk about the same set of points that make up a line. But thinking about sets, especially sets of infinite cardinality, is not taught as early as manipulating equations, so understanding a graph (a set of points in the plane) as an equation instead of as a set of points defined by that equation (and described equally well by another property) is probably a better first description. It's also the case that if you want to do certain things with lines like say find where they intersect, you're going to do that with equations. Even if you defined your lines with the coordinates/set notation, you'll use equations to find the intersection. So you may as well start with equations instead of needing to switch to them once you need them. But it's fine if you find the coordinates/set notation to be more intuitive. It's good to be able to think about things in multiple ways, and to be able to think through converting between them.
