The population growth of a city since 1900 is represented by a linear model. Interpret the slope and tje y intercept
The slope of the linear model represents the rate at which the population of the city is growing. It tells us how much the population increases (or decreases) on average for each unit increase in time (in this case, each year since 1900).
For example, if the slope is positive and equal to 100, it means that on average, the population is increasing by 100 people each year since 1900. Conversely, if the slope is negative and equal to -100, it means that on average, the population is decreasing by 100 people each year since 1900.
The y-intercept of the linear model represents the initial population of the city in the year 1900. It indicates the population size when the time variable is zero. For example, if the y-intercept is 10,000, it means that the estimated population of the city in 1900 was 10,000 people.
The slope of a linear model represents the rate of change of the dependent variable (in this case, the population growth) with respect to the independent variable (in this case, time).
Interpreting the slope will depend on the units used for the variables involved. If time is measured in years and population growth is measured in number of people, the slope will represent the average change in population growth per year. For example, if the slope is 100, it means that the population is growing by an average of 100 people per year since 1900.
The y-intercept of a linear model represents the value of the dependent variable when the independent variable is zero. In this case, it would represent the population growth in the year 1900. However, since it is unlikely for a city's population growth to be zero in the year 1900, the y-intercept might not have a direct practical interpretation in this context. Nonetheless, it is still a part of the linear model and helps determine the prediction for population growth at the starting point of the model.