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 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.

Answer 1

To interpret the slope and the y-intercept of the linear model representing the city's population growth since 1900, we can analyze the coordinates provided.

The points plotted on the graph indicate the population (in thousands) over time (in years since 1900). The first point is (0, 20), which suggests that in the year 1900 (at x=0), the population was 20,000 people (20 in thousands).

Now, let's calculate the slope of the line. The coordinates given can be used to compute the slope (m) using the formula:

\[ m = \frac{(y_2 - y_1)}{(x_2 - x_1)} \]

Using two points, for example (0, 20) and (60, 57):

\[ m = \frac{(57 - 20)}{(60 - 0)} = \frac{37}{60} \approx 0.617 \]

This slope indicates that the population increases by approximately 0.617 thousand people (or 617 people) for every year since 1900.

Now, interpreting the options provided based on this information:

1. The slope suggests that for each year, the population increases by about 600 people (if rounded), which does not match the first option.
2. The y-intercept (20) reflects the population in 1900, indicating that the population was 20,000 at that time.

Therefore, the closest matching option based on the derived slope and intercept is:

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

This option correctly states a y-intercept of 20,000 for the population in the year 1900. It may not precisely match the calculated slope but is the most reasonable interpretation from the provided choices.