flutterflies
PLEASE HELP! At a corner gas station, the revenue R varies directly with the number g of gallons of gasoline sold. If the revenue is $24.25 when the number of gallons sold is 5, find a linear equation that relates revenue R to the number of g of gallons of gasoline. then find the revenue R when the number of gallons of gasoline sold is 13.5.
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mjr632
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Hello, do you understand how to find the equation of a line?
mjr632
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y=mx+b
flutterflies
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so how will the variables fit into the equation?
mjr632
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Okay, we need two points to find the slope of the linear equation
mjr632
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Our first point shall be (5, 24.25)
mjr632
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Can you think of another point that we can intuitively know given the question?
flutterflies
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(x, 13.5) doesn't give the x value
mjr632
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Okay, we know how much revenue the company makes when they sell 0 gas, correct?
flutterflies
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sure.
mjr632
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How much revenue will they make when they sell 0 gas?
flutterflies
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wouldn't it just be 0
mjr632
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Correct
mjr632
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the equation for the slope of a line is \[m=\frac{y_1-y_2}{x_1-x_2}\]
mjr632
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We now have two points (0,0) and (5, 24.25)
mjr632
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Do you see how if we plug in these two points, we can obtain the slope m?
flutterflies
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slope would be 4.85
mjr632
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correct
mjr632
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We know that the equation for a line is y = mx + b
mjr632
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and we have the value of m
mjr632
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we also have the value for y and x
mjr632
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which are (5, 24.25)
mjr632
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If we plug in these values, m, x and y, then all we have to find is b
flutterflies
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would the equation be y= 4.85x+48.5?
mjr632
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no
mjr632
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24.25 = (4.85)(5)+b
mjr632
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24.25 = 24.25+b
mjr632
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Do you see what b must equal?
flutterflies
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b=0
mjr632
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Correct
mjr632
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We now have the full equation
flutterflies
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equation will be y=4.85x+0
mjr632
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You got it
mjr632
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Now you just need to find y = 4.85(13.5)
flutterflies
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wouldn't the 13.5 be in place of y and not x since the point is (x, 13.5)
mjr632
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no, the amount of gas is your x variable
mjr632
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the profit is your y value
flutterflies
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so the answer would be 65.47
mjr632
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Correct
flutterflies
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Thank you!!!!
mjr632
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You're welcome, good work!
mjr632
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Did you need any help with any other questions?