Final answer:
For a linear function to be an appropriate model for a data set with an independent and dependent variable, the data set must be continuous and have a linear relationship between the variables, as depicted by a straight-line relationship on a scatter plot. This scenario is best represented by Option A.
Step-by-step explanation:
To determine the appropriate model for a data set with an independent and dependent variable, we look for the type of relationship that they share. For a linear function to be an appropriate model, there must be a linear relationship between the variables. This relationship is evident when the rate of change is constant, which is reflected graphically by a straight-line plot on a scatter diagram. The nature of the data set, whether it is continuous or discrete, does not solely determine the use of a linear model, although continuous data is more often associated with linear models. Thus, for a linear function to represent the data accurately, the statement that must hold true is: The data set is continuous, and the relationship between the variables is linear (Option A).
A linear equation such as y = a + bx can represent this relationship, where a is the y-intercept and b is the slope of the line. The distinction between the independent and dependent variables is that the independent variable (usually represented as x) is the variable that we control or that acts as the input, and the dependent variable (usually represented as y) is the output or the variable that we observe in response to changes in the independent variable.