Question

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

Answer 1

Not all lines are proportional and have a set ratio

Answer 2

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".