Question

The monthly cost (in dollars) of water use is a linear function of the amount of water used (in cubic meters, m^3). The cost for using 32 m^3 of water is $43.31, and the cost for using 45 m^3 is $60.86. What is the cost of using 44 m^3 of water?

Answer 1

To calculate the cost of using 44 cubic meters of water, a linear equation based on the provided data points is derived. The cost is found to be $60.62.

Step-by-step explanation:

To find the cost of using 44 m3 of water, we first need to determine the linear equation that represents the relationship between the amount of water used and the cost.

We are given two points: (32, 43.31) and (45, 60.86), where the first component of each pair represents the amount of water used in cubic meters, and the second component represents the cost in dollars.

Step 1: Find the slope (m) of the line using the formula m = (y2 - y1) / (x2 - x1). Plugging in our values, we get m = (60.86 - 43.31) / (45 - 32) = 17.55 / 13 = 1.35.

Step 2: Use the point-slope form of a line (y - y1) = m(x - x1) with one of the given points to find the equation. Let's use the first point (32, 43.31): y - 43.31 = 1.35(x - 32).

Step 3: Express the equation in slope-intercept form (y = mx + b). y = 1.35x + (43.31 - 1.35(32)) = 1.35x + 0.71.

Step 4: Now we can find the cost for using 44 m3 by plugging x = 44 into the equation: y = 1.35(44) + 0.71 = 59.91 + 0.71 = $60.62.

Therefore, the cost of using 44 m3 of water is $60.62.