1. The problem states there is a linear relationship between the number of people in tens of millions living in urban areas in the US and the number of years since 1960.
2. We are given two points on the line: $(0,6)$ and $(25,13)$, where the first coordinate is years since 1960 and the second is tens of millions of people.
3. To find the equation of the line, we first calculate the slope $m$ using the formula:
$$m=\frac{y_2 - y_1}{x_2 - x_1} = \frac{13 - 6}{25 - 0} = \frac{7}{25} = 0.28$$
4. Using the point-slope form $y - y_1 = m(x - x_1)$ and the point $(0,6)$:
$$y - 6 = 0.28(x - 0)$$
$$y = 0.28x + 6$$
5. This equation models the number of people in tens of millions living in urban areas as a function of years since 1960.
6. The slope $0.28$ means the urban population increases by 0.28 tens of millions (2.8 million) per year since 1960.
7. The y-intercept $6$ means at year 0 (1960), the urban population was 60 million.
Final answer:
$$y = 0.28x + 6$$ where $y$ is tens of millions of people and $x$ is years since 1960.
Urban Population
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