Final answer:
The correct equation for the budget line with T on the vertical axis, based on the provided options and understanding of budget constraints, is unclear as the question does not provide enough contextual information about the prices and income. A budget line equation would indicate the trade-off between dancing and the other good, S, represented by a negative slope in the equation.
Step-by-step explanation:
To find the equation for a budget line with T (the number of times she goes dancing per month) on the vertical axis, we need to understand the underlying budget constraint. A budget constraint reflects all the combinations of goods that a consumer can afford given their income and the prices of goods. Using the provided details from José's budget constraint example, we can relate the general concept to the student's question.
José has $56 and faces two prices: $14 for T-shirts and $7 for movies. Therefore, the vertical intercept is the number of movies he could buy if he spends all his money on movies, which is $56 divided by $7, giving us 8 movies. Similarly, the horizontal intercept is $56 divided by $14, which gives us 4 T-shirts (all money spent on T-shirts, no movies). The slope of this line, calculated as rise/run or change in Y over change in X, is -8/4, which simplifies to -2.
Applying this example to the student's question, we need an equation with a slope that represents how many times she goes dancing relative to another good, denoted by S. Based on the options provided, the correct equation must have a negative slope indicating that if the student chooses to go dancing more times, she must consume less of the other good, S.