Final Answer:
A scenario can be represented by a linear function when one quantity changes at a constant rate per unit interval relative to the other quantity, which corresponds to option 1.
Therefore, correct option is 1) When one quantity changes at a constant rate per unit interval relative to the other quantity.
Step-by-step explanation:
Linear functions depict a constant rate of change between two variables. In the context of scenarios, this means that for every unit change in one quantity, there is a consistent and fixed change in the other quantity. This relationship is characterized by a straight-line graph.
Options 2, 3, and 4 describe situations where the rate of change is not constant. In option 2, the rate varies, making it nonlinear. Option 3 involves exponential growth or decay, which results in a nonlinear function. Option 4, with changes occurring randomly, lacks a systematic pattern and cannot be represented by a linear function.
Understanding the conditions for linear functions is fundamental in mathematical modeling and analysis, enabling accurate representations of relationships between variables.
Therefore, correct option is 1) When one quantity changes at a constant rate per unit interval relative to the other quantity.