Use the image to answer the question.

Question

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

A.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.

B.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.

C.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.

D.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.
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Answer 1

To interpret the slope and y-intercept of the linear model representing population growth, we can analyze the graph's details provided.

1. Y-Intercept: The point where the line crosses the y-axis is approximately at (0, 20). This indicates that in the year 1900 (0 years since 1900), the population of the city was 20,000 (since the population is given in thousands).

2. Slope: To find the slope of the line, we need to determine the change in population per change in years. From the given data points, we can calculate the slope using two points, for example (0, 20) and (80, 66).

   • Change in population = 66 - 20 = 46 (thousand)
   • Change in years = 80 - 0 = 80

   Slope = Change in population / Change in years = 46 / 80 = 0.575 (thousand per year)

This means that the population grows by approximately 0.575 thousand people (or about 575 people) for every year since 1900.

Conclusion

The correct interpretation from the options given is:

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

(Note: The slope calculated does not seem to match precisely with a given option; the closest estimate would indicate that the options may contain approximations or adjustments.)