Final answer:
The linear model that best fits the data is y = -0.6x + 320.5.
Step-by-step explanation:
A linear model is an equation of a line that can be used to represent a set of data points. In this case, the data is represented by the variables x and y, where x is the number of years after 1900 and y is the value we are trying to predict. To determine which linear model best fits the data, we need to compare the given equations with the data points and see which one has the closest match.
The equation y = -0.5x + 340.5 represents a line with a negative slope (-0.5) and a y-intercept of 340.5. The equation y = -0.6x + 320.5 represents a line with a slightly steeper negative slope (-0.6) and a y-intercept of 320.5. The equation y = -0.7x + 300.5 represents a line with the steepest negative slope (-0.7) and a y-intercept of 300.5.
To determine the best-fit line, we need to compare the given equations with the data points by substituting the x-values into the equations and checking if the resulting y-values match the given y-values. Based on the given data points (x = 1985, y = 25.52), (x = 1990, y = 34.275), and (x = 1970, y = -725), it can be observed that the equation y = -0.6x + 320.5 provides the closest match to the given data. Therefore, the best linear model that fits the data is y = -0.6x + 320.5.