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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 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.
For every year since 1900, the population grew by approximately 300. In 1900, the population was 0.
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Answer 1

To interpret the slope and the y-intercept from the given information, we need to analyze the points plotted and what they represent.

1. Y-Intercept: At the year 1900 (represented by 0 on the x-axis), the population is approximately 20 (which means 20,000 when converted from per thousand). This indicates that in 1900, the population of the city was 20,000.

2. Slope: To find the slope, we can approximate the change in population per year from the graph. Looking at the plotted points:

   • Between years 0 (population 20) and 80 (population 66), the change in population is (66 - 20) = 46 over a span of 80 years.
   • So the slope can be calculated as the change in population per year: 46/80 = 0.575 (which when converting to per 1000 would be approximately 575).

Given this analysis, the response that closely aligns with the interpretation of the slope and the y-intercept is:

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

The slope being approximately 650 seems more applicable than the calculations shown but overall the interpretation is correct given how we apply it to the context and units.

However, note that the values provided in the options might have some approximations thus finding the exact number could vary. Since the closest given option that aligns with our analysis in understanding real population growth and initialization is this.