It's been awhile since I've taken introductory microeconomics. I read budget lines can be discontinuous awhile ago but am suspicious as to such a concept being discussed in intro micro classes particularly calling them budget 'lines'.
The problem:
Say Jill likes food and clothing. Jill has 200 to spend on food and clothing. One unit of food costs \$1 while one unit of clothing costs $2.
Budget line is 200=F+2C
Say Jill receives an 80% discount on food but it applies up to 100 units.
New budget line is 200=0.2F+2C for 0-100 then same as old for 100 onward?
So it's discontinuous? So it's not really a budget 'line' right (though piecewise, it's a line, I guess).