Final answer:
The constant of proportionality in the equation y = 2.30x is 2.30, which signifies the cost per pound of nails. This value is the ratio of the cost to the weight of the nails, representing a direct proportional relationship.
Step-by-step explanation:
The cost, y, for x pounds of nails can be represented by the equation y = 2.30x. The constant of proportionality in this equation is the coefficient of x, which is 2.30. This constant tells us how much the cost y increases for every additional pound of nails. It represents the cost per pound of nails.
In a proportional relationship like this one, the constant of proportionality is the ratio of the two variables when they are directly related to each other. In the equation y = 2.30x, for every one unit increase in x, y increases by 2.30 units. Thus, if you buy 1 pound of nails, it will cost you $2.30, and if you buy 2 pounds of nails, it will cost you $4.60, and so on. This linear equation shows that the cost is directly proportional to the weight of the nails purchased.
The constant of proportionality is a mathematical concept that relates two variables in a proportional relationship. In direct proportion, it is the fixed value that, when multiplied by one variable, yields the other. Represented by the letter k, it maintains the ratio between the quantities. For instance, in the equation y=kx, k is the constant of proportionality. It signifies the rate at which one variable changes concerning the other. This concept is fundamental in understanding linear relationships, such as in physics, finance, and other fields where proportional connections exist between quantities.