A single parent earning $8 an hour with 2,500 hours available faces the lower budget line: all leisure and no income at the right, 2,500 hours of work and $20,000 at the left. The preferred choice is 2,000 hours of work, 500 hours of leisure and $16,000 of income.
Now guarantee the family $18,000 and take away a dollar of support for every dollar earned. The budget line goes flat: the family has $18,000 whether it works zero hours or two thousand. Only past about 2,300 hours of work does income rise above the guarantee at all. Withdrawing the support more slowly, 50 cents on the dollar, tilts the line back upward, so an extra hour of work is worth $4 rather than nothing. The family can then choose a point like R, working as much as before for more income, or S, working less for more income than it started with. The slider sets how fast the support is withdrawn.