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The monthly cost (in dollars) of water use is a linear function of the amount of water used (in hundreds of cubic feet, HCF). The cost for using 14 HCF of water is $39.89, and the cost for using 51 HCF is $100.94. What is the cost for using 21 HCF of water?

The monthly cost (in dollars) of water use is a linear function of the amount of water used (in hundreds of cubic feet, HCF). The cost for using $14$ HCF of water is $\$39.89$ , and the cost for using $51$ HCF is $\$100.94$ . What is the cost for using $21$ HCF of water?

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Evaluate two-variable equations: word problems

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Q. The monthly cost (in dollars) of water use is a linear function of the amount of water used (in hundreds of cubic feet, HCF). The cost for using

14

HCF of water is

\$39.89

, and the cost for using

51

HCF is

\$100.94

. What is the cost for using

21

HCF of water?

Calculate slope: Calculate the slope of the cost function. $\newline$ We have two points: $(14, 39.89)$ and $(51, 100.94)$ . $\newline$ Slope $(m) = \frac{\text{Change in cost}}{\text{Change in HCF}} = \frac{100.94 - 39.89}{51 - 14} = \frac{61.05}{37} = 1.65$
Find y-intercept: Find the y-intercept $b$ of the linear equation. $\newline$ Using the point $(14, 39.89)$ and the slope $1.65$ : $\newline$ $39.89 = 1.65(14) + b$ $\newline$ $b = 39.89 - 23.1 = 16.79$
Write equation: Write the equation of the line. $\text{Cost} = 1.65(HCF) + 16.79$
Calculate cost: Calculate the cost for $21$ HCF. $\newline$ Cost = $1.65(21) + 16.79$ $\newline$ Cost = $34.65 + 16.79 = 51.44$

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