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

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 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 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 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.

Answer 1

To analyze the slope and y-intercept of the linear model for the city's population growth, we identify the coordinates given and the general characteristics of linear models.

The points plotted indicate the changes in population over the years. The y-coordinate (population per thousand) at the beginning (when x = 0, meaning the year 1900) is 20. Therefore, the y-intercept is 20.

The slope can be determined by examining two points on the line, for example, (0, 20) and (80, 66):

1. Calculate the change in population (rise):

   • From 20 to 66 (population per thousand), the change is 66 - 20 = 46.

2. Calculate the change in years (run):

   • From 0 to 80, the change is 80 - 0 = 80 years.

3. Calculate the slope:

   • Slope = Rise / Run = 46 / 80 = 0.575.

This suggests that for every year since 1900, the population increases by approximately 0.575 thousand people (or approximately 575 people) per year.

Taking the values discovered:

• In 1900 (x = 0), the population was 20,000 (20 thousand).
• The growth per year is approximately 575 people.

None of the provided options match the exact slope we computed, but based on the closest approximation, the option that fits best is:

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

This is the best answer, acknowledging that it represents a generalization rather than the exact calculation.