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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 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.

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.
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Answer 1

To interpret the slope and the y-intercept of the linear model based on the information given:

1. Y-Intercept: The y-intercept occurs at the point when \( x = 0 \). From the given coordinates, the y-value at this point (in the year 1900) is approximately 20. The graph indicates the population was 20,000 (since the y-axis is in thousands).

2. Slope: The slope of the line represents the rate of change of population per year. To calculate the slope, we observe the change in population (y-values) over the change in years (x-values).

From the points given:

• The y-value at \( x = 0 \) (in 1900) is 20.
• The y-value at \( x = 60 \) (in 1960) is approximately 57.

The change in population from 20 to 57 is:

\[ \text{Change in Population} = 57 - 20 = 37 \text{ (in thousands)} \]

The change in years from 0 to 60 is:

\[ \text{Change in Years} = 60 - 0 = 60 \]

Thus, the slope (rate of population increase per year) is calculated as:

\[ \text{Slope} = \frac{\text{Change in Population}}{\text{Change in Years}} = \frac{37}{60} \approx 0.617 \text{ (in thousands)} \]

This means, approximately, that for every year since 1900, the population increased by about 617 individuals. Since the population in thousands is used, this means approximately 617 more individuals per year.

Now, we can match these interpretations to the options provided:

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

This interpretation aligns best based on the calculations and information provided in the question.