Proportional Relationships

A proportional relationship is a relationship between two quantities where the ratio of one quantity to the other quantity is constant.

The constant of proportionality is the constant value (k) that relates two proportional quantities, often expressed in the equation p = kw.

To find the constant of proportionality, isolate k in the equation p = kw, which gives k = p/w.

The unit rate is a comparison of two different quantities when they are combined together, expressed as a quantity per one unit of another quantity.

To calculate the unit rate, divide the total quantity by the number of units. For example, if 405 rotations occur in 5 minutes, the unit rate is 405 ÷ 5 = 81 rotations per minute.

A graph is proportional if it passes through the origin (0,0) and shows a straight line, indicating a constant ratio between the two variables.

The equation for a proportional relationship is typically written as p = kw, where p is the dependent variable, w is the independent variable, and k is the constant of proportionality.

The job pays $7 per hour, calculated by dividing $56 by 8 hours.

The point (2, 94) represents that after 2 weeks, they save $94.

A relationship is proportional if the ratios of corresponding values are constant across the table.