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An illustration shows the first quadrant of a coordinate plane titled Population of a City Since 1900.
The x-axis shows years since 1900 and ranges from 0 to 80 in increments of 10. The y-axis shows population per thousand and ranges from 0 to 80 in increments of 5. Nine points are plotted on the graph. The points are plotted at approximate coordinates left parenthesis 0 comma 20 right parenthesis, left parenthesis 10 comma 28 right parenthesis, left parenthesis 20 comma 30 right parenthesis, left parenthesis 30 comma 35 right parenthesis, left parenthesis 40 comma 47 right parenthesis, left parenthesis 50 comma 55 right parenthesis, left parenthesis 60 comma 57 right parenthesis, left parenthesis 70 comma 68 right parenthesis, and left parenthesis 80 comma 66 right parenthesis. An upward slanting line starts at left parenthesis 0 comma 20 right parenthesis and continues to left parenthesis 60 comma 57 right parenthesis.

The population growth of a city since 1900 is represented by a linear model. Interpret the slope and the y
-intercept.

(1 point)
Responses

For every year since 1900, the population grew by approximately 300. In 1900, the population was 0.
For every year since 1900, the population grew by approximately 300. In 1900, the population was 0.

For every year since 1900, the population grew by approximately 1,590. in 1900, the population was 20,000.
For every year since 1900, the population grew by approximately 1,590. in 1900, the population was 20,000.

For every year since 1900, the population grew by approximately 650. In 1900, the population was 20,000.
For every year since 1900, the population grew by approximately 650. In 1900, the population was 20,000.

For every 0.65 of a year since 1900, the population grew by approximately 1,000. In 1900, the population was 20,000.
For every 0.65 of a year since 1900, the population grew by approximately 1,000. In 1900, the population was 20,000.
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Answer 1

To interpret the slope and the y-intercept of the linear model for the population growth of the city since 1900, we need to extract the relevant information from the data provided.

1. Slope (m):

   • The slope represents the change in population per unit of time (in this case, years).
   • From the provided points, we can look at the difference in population and the difference in years to determine the slope.
   • Based on the values you provided, if we calculate the approximate change in population from your first plotted point (0, 20) to your last plotted point (80, 66), we see an increase in population.
   • The change in y (population) is approximately \(66 - 20 = 46\) (in thousands), and the change in x (years) is \(80 - 0 = 80\).
   • Therefore, the slope is calculated as \(\frac{46}{80} \approx 0.575\) (in thousands per year). Multiplying by 1,000 gives us about 575,000 people per year.

2. Y-Intercept (b):

   • The y-intercept represents the estimated population at the starting year, 1900.
   • From your first plotted point (0, 20), we see that when \(x = 0\) (the year 1900), the population is 20. This indicates that in 1900, the population was approximately 20,000.

From this understanding, we can conclude:

• The slope indicates that the population is growing at a rate of about 575 people per year.
• The y-intercept tells us that the population in 1900 was approximately 20,000.

None of the exact choices you listed exactly match this analysis, but the closest interpretation would be:

For every year since 1900, the population grew by approximately 650. In 1900, the population was 20,000.

This indicates that one of the options may slightly round or interpret the slope.