Question

The equation y = kx represents a proportional relationship between x and y, where k is the constant of proportionality. For a moving object, the equation d = st represents a proportional relationship between distance (d) and speed (s) or between distance (d) and time (t). Explain the different ways that you can define the constant of proportionality for this equation. Then describe some other equations that represent proportional relationships in the real world and explain why they’re useful. Research on the Internet, if needed.

Answer 1

notice how if you compare

y = kx
and
d = st

they follow the same pattern. therefore, "s" corresponds to the constant of proportionality k.

if you solve for s, you get s = d/t, or distance/time. in layman's terms we call this the speed.

Answer 2

As for a real-life example, I'll give you *one* and let you come up with/research others on your own.

Generally, when you go to a store and buy the same item, each item costs the same amount. at 0 items, you don't need to pay anything. at 1 item, you pay 1 * the cost of the item. at 2 items, you pay 2 * the cost of the item.

the cost of the item acts as a k-value.