constant of proportionality, unit rate
TEKS 7(1)(D), 7(1)(G), 7(4)(A), 7(4)(C)
Recall that two quantities x and y have a proportional relationship if y is always a constant multiple of x. This constant multiple is called the constant of proportionality.
If x and y have different units, then the constant of proportionality can be written as a unit rate.
Each brick shown has a length of 20 cm. The proportion total length of one brick to the number of bricks is 20 to 1, so the unit rate is 20. The proportion remains the same as bricks are added. The final proportion is 100 to 5, so the unit rate is still 20.
The constant of proportionality is 20 cm per brick. This is a proportional relationship, so the constant of proportionality and the rate of change are the same number.
TEKS 7(1)(A), 7(1)(D), 7(4)(A), 7(4)(C)
Example Finding Constants of Proportionality
The weight of the stack depends on the number of books in the stack. Identify the constant of proportionality for this situation. Then use the constant of proportionality to find the weight of 11 books.
The constant of proportionality is the ratio y over x where x is the independent variable and y is the dependent variable.