Definition
Constant of proportionality
The constant of proportionality is the fixed multiplier connecting two quantities in a proportional relationship.
What it means
When one quantity is always the same number of times another, that unchanging number is the constant of proportionality. You can find it by dividing y by x for any nonzero input. Its units tell you how much y there is for one unit of x.
Remember it
Same multiplier for every pair.
Example
Five notebooks cost $17.50. Let x be notebooks and y be cost. The constant of proportionality is k = 17.50 ÷ 5 = 3.50, so y = 3.50x. The rate is $3.50 per notebook.
Watch for
The relationship y = x + 3 is not proportional because y ÷ x changes with x and the equation has an added amount instead of only a fixed multiplier.
Common mix-up
The constant of proportionality is the multiplier k, not a single output value y. In y = 3.5x, k is 3.5 for every pair.
Exact meaning
In a proportional relationship written y = kx, k is the constant of proportionality. For any pair with x ≠ 0, k = y ÷ x, so the same output-to-input ratio holds throughout the relationship.