Additive vs. Multiplicative

Additive relationships involve adding a constant to a variable (y = x + a), while multiplicative relationships involve multiplying a variable by a constant (y = kx).

An additive relationship is identified by a straight line that does not pass through the origin, indicating a constant addition to the variable.

The general form is y = x + a, where 'a' is a constant.

The general form is y = kx, where 'k' is a constant.

A multiplicative relationship is identified by a straight line that passes through the origin, indicating a constant ratio.

If a graph crosses through the origin, it indicates a multiplicative relationship, where the output is directly proportional to the input.

This equation represents a multiplicative relationship because it can be rewritten as y = 2x.

In an additive relationship, the output increases by a constant amount 'a' regardless of the input.

In a multiplicative relationship, the output also doubles if the input doubles, as it is directly proportional.

A real-world example of an additive relationship is calculating total cost by adding a fixed shipping fee to the price of items.