An illustration shows the first quadrant of a coordinate plane titled Population of a City Since 1900.

Question

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 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 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.
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Answer 1

To interpret the slope and y-intercept of the linear model for the population growth of the city since 1900, we can derive the following from the provided data:

1. Y-Intercept (Population in 1900): The y-intercept is the population at the beginning of the time period, which is at the point (0, 20) on the graph. This means in the year 1900 (x=0), the population was approximately 20,000 (since the y-axis measures population per thousand).

2. Slope (Annual Population Growth): The slope of the line shows the rate of population growth per year. To find this, we can look at the change in population (y-values) over the change in time (x-values). Using two points on the line, for example, (0, 20) and (60, 57):

   • Change in y = 57 - 20 = 37 (thousands)
   • Change in x = 60 - 0 = 60 (years)
   • Slope = Change in y / Change in x = 37 / 60 ≈ 0.6167 (thousands per year)

To convert this to actual numbers per year:

• 0.6167 thousand = 616.7 people Round off to approximately 650 people.

Final Interpretation:

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

So, the correct response is: For every year since 1900, the population grew by approximately 650. In 1900, the population was 20,000.