Definition: The constant of proportionality is the constant ratio y/x in a proportional relationship, the number k in the equation y = kx.
What is it?
In a proportional relationship, every pair of values has the same ratio. That unchanging ratio is the constant of proportionality, written k.
How do you find it?
Divide y by x for any pair in the table. If Mathbot buys 7 pounds of bolts for 31.50 dollars, then k = 31.50 / 7 = 4.50 dollars per pound.
How do you use it?
Write y = kx, here y = 4.5x. To price 12 pounds, calculate 4.5 x 12 = 54 dollars. To find how many pounds 99 dollars buys, solve 4.5x = 99, so x = 22 pounds.
Where is it on a graph?
It is the unit rate, the y-value when x is 1, and it equals the slope of the line through the origin.
What are common mistakes?
Dividing x by y gives the reciprocal, which is also a constant but answers a different question: pounds per dollar, about 0.22. State which quantity is per one unit. Another slip is using the constant when the relationship has a fixed starting fee.
Where to learn it
- Writing and Using y = kx Equations – lesson
- Spotting Proportional Relationships in Tables and Graphs – lesson