Banquet Cost
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Slope or Rate of Change: The cost function for the banquet can be expressed as: \[ C(x) = 95 + 15x \] where:
- \(C(x)\) is the total cost,
- \(x\) is the number of people attending.
The slope (rate of change) is the coefficient of \(x\), which is 15.
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Meaning of the Slope in Context: In the context of the school banquet, the slope of 15 indicates that for each additional person attending the banquet, the total cost increases by $15. This reflects the per-person cost associated with the banquet expenses.
Home Prices in Brainerd County
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Slope or Rate of Change: To find the slope (rate of change) of home prices from 1980 to 1986, we first note the two data points:
- In 1980: \(y_1 = 97,000\)
- In 1986: \(y_2 = 109,000\)
The years can be treated as \(x_1 = 0\) (1980) and \(x_2 = 6\) (1986). The formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is: \[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{109,000 - 97,000}{6 - 0} = \frac{12,000}{6} = 2,000 \]
Thus, the slope is $2,000.
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Meaning of the Slope in Context: In the context of home prices in Brainerd County, the slope of $2,000 indicates that the average price of a home increased by $2,000 per year from 1980 to 1986. This signifies a steady rise in housing prices during that six-year period.