To properly interpret the slope and the y-intercept of a linear model for population growth, we need to understand what these terms usually represent in the context of the equation of a line, typically expressed as \(y = mx + b\), where:
- \(m\) is the slope, and it represents the rate of change of the population with respect to time (in this case, years since 1900).
- \(b\) is the y-intercept, and it represents the initial population at the start of the time period, which in this case would be the year 1900.
Given the options provided, we can determine the following:
-
If the slope is approximately 300, it implies that the population is growing by about 300 people each year. However, the initial population given would have to be 0, which is unlikely.
-
If the slope is approximately 650, it suggests the population grows by 650 people each year. The y-intercept of 20,000 indicates that the population was 20,000 in 1900, which might be plausible.
-
The next set of options discusses a different slope (for \(0.65\) years) and a y-intercept of 20,000, which seems less common in typical population growth discussions.
-
Finally, there is another choice with a larger slope of approximately 1,590 and the same y-intercept of 20,000.
Conclusion:
Without additional context or calculations, the most reasonable interpretation based on typical population growth modeling would likely be:
"For every year since 1900, the population grew by approximately 650. In 1900, the population was 20,000."
This option provides a clear and plausible scenario where the linear growth is consistent with a realistic population growth pattern.