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The slope of the budget constraint tells us the rate at which our consumer can substitute units of the good graphed on the horizontal axis for units of the good on the vertical axis.
An evening at the movies costs our consumer $40 and an evening at her favorite club costs her $60. So, for each movie she gives up she has $40 more to spend (2/3 the price of a club visit). The slope of the budget constraint is the same as the negative of the ratio of the prices, so the slope is - 40/60 = - 2/3. The slope is negative because to consume more of one good she must consume less of the other.
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