The equation Y equals 4X gives the relationship between the number of goats X and the number of bales of hay need a per day why what is the constant of proportionality? What does it mean in this context?

Answer 1

In the equation \( Y = 4X \), \( Y \) represents the number of bales of hay needed per day, and \( X \) represents the number of goats.

The constant of proportionality in this relationship is 4. This means that for every goat (1 goat), you need 4 bales of hay per day.

In this context, the constant of proportionality indicates how much hay is needed for each goat. Specifically, it tells you that regardless of how many goats you have, the amount of hay needed grows in proportion to the number of goats: for 1 goat, you need 4 bales of hay; for 2 goats, you need 8 bales of hay (\(4 \times 2\)); for 3 goats, 12 bales (\(4 \times 3\)), and so on. This relationship reflects a direct correlation between the number of goats and the amount of hay required, demonstrating the importance of this constant in managing resources effectively.