The population growth of a city since 1900 is represented by a linear model. Interpret the slope and the y intercept
In the context of a linear model representing the population growth of a city since 1900, the slope of the model represents the rate of change in population over time. It indicates how much the population is expected to increase or decrease for each unit increase in time.
If the slope is positive, it means that the population is expected to grow at a certain rate over time. For example, if the slope is 500, it means that the population is expected to increase by 500 people every year since 1900.
If the slope is negative, it means that the population is expected to decrease at a certain rate over time. For example, if the slope is -200, it means that the population is expected to decrease by 200 people every year since 1900.
The y-intercept of the model represents the starting population at the year 1900. It indicates the population size before any growth or decline occurred. For example, if the y-intercept is 10,000, it means that in the year 1900, the city had a population of 10,000 people.
The slope and y-intercept in a linear model represent important characteristics of the population growth of a city since 1900.
1. Slope: The slope of the linear model represents the rate of change in the population growth of the city over time. It indicates how much the population of the city is increasing or decreasing each year. A positive slope suggests that the population is growing, while a negative slope indicates a declining population. The magnitude of the slope indicates the steepness of the growth or decline.
2. Y-intercept: The y-intercept of the linear model represents the population of the city at the starting point, which is 1900 in this case. It gives an estimate of the initial population when the data collection began. The y-intercept provides a reference point to understand the population growth from its starting point. It might represent the city's population before any significant changes or events that could impact its growth.
By considering both the slope and y-intercept in the linear model, you can analyze and interpret the population growth pattern of the city since 1900.