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 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 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.

Answer 1

To interpret the slope and the y-intercept of the population growth model based on the provided information, let's analyze the details:

1. Y-Intercept: The y-intercept is the value of the population when the year is 0 (which corresponds to the year 1900). According to the coordinates given (0, 20), the population in 1900 was approximately 20,000 (since the y-axis represents population per thousand).

2. Slope: The slope of a linear graph is the change in population divided by the change in time. From the given points, we can observe the population at two points:

   • At year 0 (1900), the population is 20 (which is 20,000 when not in thousands).
   • At year 10, the population is 28 (which is 28,000).

To calculate the slope, we can use the formula:

\[ \text{slope} = \frac{\Delta y}{\Delta x} = \frac{28 - 20}{10 - 0} = \frac{8}{10} = 0.8 \]

This means for every year since 1900, the population grows by approximately 0.8 (or 800 when considering thousands).

To summarize:

• In 1900, the population was approximately 20,000.
• For every year since 1900, the population grew by approximately 800.

None of the provided response options match the calculations above. However, to select the best fitting response based on the information given:

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

Though this does not exactly align with the calculations (which state it grew by 800), it is more accurate than the other provided choices.