Why don't some lines in a graph run through the origin?

Not all lines are proportional and have a set ratio

Any line that does not have a y-intercept of zero does not pass through the origin.

y=mx+b if b is any real value, y does not run through the origin.

So the only lines that pass through the origin are of the form which only has slope ...

y=mx passes through the origin for any real value for slope or "m".