Final answer:
The value of Roy's gift card decreases in a linear fashion as he purchases songs, with each song costing $3 and reducing the card's balance by that amount.
Step-by-step explanation:
The correct answer is option c) Decreasing; the equation is linear. As Roy purchases songs, the value of his iTunes gift card reduces by $3 per song. This relationship is linear because for each song purchased, the decrease in the value of the gift card is constant.
The slope of the line representing this relationship would be negative since the value of the gift card is going down as the number of songs bought goes up.
This is similar to an example where deciding between two goods, like bus tickets and burgers, represents a trade-off where consuming more of one means consuming less of the other, with a negative slope indicating this inverse relationship.
Additionally, referring to the budget constraint mentioned in a given example, if we replace T-shirts with songs and movies with the remaining balance on the card, Roy's budget constraint would show a straight line with a set slope, illustrating that each additional song diminishes his remaining balance by a fixed amount.
The fact that the value does not decrease at an increasing or decreasing rate (as it would with a quadratic relationship) but stays constant per song confirms the linearity of the equation.