Final answer:
The equations demonstrate direct proportionality and each one can be matched with a situation to show the relationship between variables. The constant of proportionality indicates the rate of change between the quantities.
Step-by-step explanation:
The equations given are examples of direct proportionality, where y changes with x based on a constant of proportionality, often referred to as k. Let's match each equation to the corresponding situation:
A. y = 3x could describe Situation 3, where for every hat (x), you pay $3 (y), which is a "4 for $10" sale reduced to a unit rate of "1 for $3" by dividing both the number of hats and the total cost by 4.
B. 1/2x = y could describe Situation 4, where for every 48 cookies baked (x), students get 24 (y). This is because 1/2 of 48 is 24, showing that there are half as many portions as cookies.
C. y = 3.5x matches Situation 1, where after 20 loads of dirt (x), there are 70 square feet (y). This means for each load, there is 3.5 square feet of dirt.
D. y = 5/2x corresponds to Situation 2, where there are 2 cups of salt for every 5 cups of water. Rearranging this gives us 5 cups of water for every 2 cups of salt, or 5/2 times the amount of salt.
The constant of proportionality represents how much one quantity changes with respect to another. In these examples, it is the number that is multiplied by the independent variable (x) to get the dependent variable (y). It provides a simple way to calculate one quantity if you know the other one.