When is it appropriate to model data with a linear function? give an example of real-world data that can be modeled with a linear function. include the linear function and a sample of the data.

Data may be modeled with a linear function when the laws of physics say so.

The following example illustrates the point.
Consider a beaker of water, initially at temperature 25°C, heated by an electrical resistance placed n the water. The beaker is well insulated so that all heat generated raises the temperature of the water.

This is illustrated in the figure below.

The current produces thermal energy of magnitude x cal, which may be considered as the independent variable.
The measured rise in temperature, y °C, is the dependent variable.

The laws of physics say that the temperature rise of the water s proportional (linear) with respect to the heat input.
Measured data of y versus x is shown below.
x, cal:    0    10    20    40   60    80   100
y, °C:   25   38    57    90   117   142    176
 
By performing a linear regression fit to the data, a linear relation is obtained as
y = 25 + 1.5x