SOLUTION: Natural Gas. The cost of 1000 cubic feet of natural gas is $39 and the cost of 3000 cubic feet is $99 There is a linear equation that expressed the cost C in terms of the numberof

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Question 127224: Natural Gas. The cost of 1000 cubic feet of natural gas is $39 and the cost of 3000 cubic feet is $99 There is a linear equation that expressed the cost C in terms of the numberof cubic feet n. Find the equation and find the cost of 2400 cubic feet of natural gas.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
If cubic feet of gas is plotted on the horizontal axis
and the corresponding cost on the vertical axis,
we are given 2 points, (1000, 39) and (3000,99)
There is a formula you can use

the given points are (x[2],y[2]) and (x[1],y[1])
%2899+-+39%29+%2F+%283000+-+1000%29+=+%28y+-+39%29+%2F+%28x+-+1000%29
60+%2F+2000+=+%28y+-+39%29+%2F+%28x+-+1000%29
3%2F100+=+%28y+-+39%29+%2F+%28x+-+1000%29
multiply both sides by 100%2A%28x+-+1000%29
3%2A%28x+-+1000%29+=+%28y+-+39%29%2A100
3x+-+3000+=+100y+-+3900
100y+=+3x+%2B+900
y+=+%283%2F100%29x+%2B+9 or in this case,
C+=+%283%2F100%29n+%2B+9 answer
check:
See if this line goes through (1000, 39) and (3000,99)
C+=+%283%2F100%29n+%2B+9
39+=+%283%2F100%29%2A1000+%2B+9
39+=+30+%2B+9
39+=+39
OK
C+=+%283%2F100%29n+%2B+9
99+=+%283%2F100%293000+%2B+9
99+=+90+%2B+9
99+=+99
OK
Find the cost of 2400 cubic feet of natural gas.
C+=+%283%2F100%29n+%2B+9
C+=+%283%2F100%292400+%2B+9
C+=+72+%2B+9
C+=+81 dollars answer