Proportional Graphs

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

A proportional graph is a straight line that passes through the origin (0,0).

The point (x, y) represents the value of the dependent variable (y) when the independent variable (x) is at a specific value.

The constant of proportionality is the ratio of the two quantities in a proportional relationship, often represented as k in the equation y = kx.

If a graph does not pass through the origin, it indicates a non-proportional relationship.

The slope of a proportional graph represents the constant ratio between the two quantities.

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

A non-proportional graph may be a curve or a straight line that does not pass through the origin.

The cost for 3 hours would be $36, as it is a proportional relationship (12 * 3 = 36).

An example of a non-proportional relationship is a situation where a fixed fee is added to a variable cost, such as a taxi fare that includes a base charge plus a per-mile charge.