Residents of the town of Maple Grove who are connected to the municipal water supply are billed a fixed amount yearly plus a charge for each cubic foot of water used. A household using 1000 cubic feet was billed $90, while one using 1600 cubic feet was billed $105. a) What is the charge per cubic foot? b) Write an equation for the total cost of a resident's water as a function of cubic feet of water used. c) How many cubic feet of water used would lead to a bill of $130? All right, here are my attempts. I first did the whole find the slope thing. (1000, 90) , (1600, 105) (105 - 90) / (1600 - 1000) = 15/600 = 1/40 So, this means that for $1, you get 40 cubic feet. (but that isn't the question... the question is how much does 1 cubic foot cost.....) that was the first thing that confused me.. but i decided that maybe i was going in the right direction, so I tried to keep working... by trying to write the equation. y = mx + b 90 = (1/40)(1000) + b 90 = 25 + b b = 65 y = (1/40)x + 65 now that i had the equation, i plugged in a 1 for x to see what 1 cubic foot would cost. y = (1/40) (1) + 65 y = 1/40 + 65 y = $65.025 so, now i subtracted that amount from the fixed amount $65.025 - $65 = $.025 or 2.5 cents What confuses me is ... .025 = 1/40 (my slope), but i thought the slope meant 1 dollar for 40 cubic feet, now 1 cubic foot for .025 cents. And if it does work out, i just would like to know why you can switch the variables around like that so easily. so.. to continue.. i have the answers for a and b.. time to work out c. 130 = (1/40)x + 65 x = 2600 a) 2.5 cents/cubic ft b)y = (1/40)x + 65 c)2600 cubic feet of water used I think it's all correct, but i seriously want to know why the variables can be switched .. because the slope should be $1 for 40 cubic feet, and not 2.5 cents for 1 cubic foot. Yes, it does make sense, i just don't know why.. lol.. thanks in advance.