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'.
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).