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 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 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 300. In 1900, the population was 0.
For every year since 1900, the population grew by approximately 300. In 1900, the population was 0.
Skip to navigation

Answer 1

To interpret the slope and the y-intercept from the linear model representing the population growth of the city since 1900, we start with the given points.

1. Y-intercept: The y-intercept of the model represents the population in the year 1900 (when x = 0). From the graph, we see that the y-coordinate at x = 0 is approximately 20. Since the population is measured in thousands, this means that in 1900, the population was approximately 20,000 people.

2. Slope: The slope of the line can be calculated by determining the change in population (y-values) over the change in years (x-values) between two points. For instance, using the coordinates (0, 20) and (10, 28):

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

   This means that for every year since 1900, the population grew by approximately 0.8 thousand, which is 800 people.

Given these interpretations, the correct response is:

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

However, this option does not appear in the provided responses. The closest option is:

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

Although this is not precisely correct, if we were to select the closest given choice, it would likely be a point of error in the problem setup or response options.

In summary:

• The population grew by approximately 800 people per year.
• The population in 1900 was about 20,000 people.

If you have to select from the provided options, pick the last one for similarity, keeping in mind the actual calculations discussed.