To find the slope (rate of change) in the scenario, we can use the formula for slope, which is:
\[ \text{slope} = \frac{\text{change in price}}{\text{change in time}} = \frac{P_2 - P_1}{t_2 - t_1} \]
Where:
- \( P_1 \) is the price in 1980 ($97,000)
- \( P_2 \) is the price in 1986 ($109,000)
- \( t_1 \) is the year 1980
- \( t_2 \) is the year 1986
Substituting the values:
\[ \text{slope} = \frac{109,000 - 97,000}{1986 - 1980} = \frac{12,000}{6} = 2,000 \]
So, the slope is \( 2,000 \).
Interpretation in Context
The slope of \( 2,000 \) means that, on average, the price of a home in Brainerd County increased by $2,000 per year between 1980 and 1986. This indicates a steady rise in the home prices during that period, reflecting either an increase in demand for homes or other market factors driving up values.
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