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flutterflies

  • 3 years ago

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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  1. mjr632
    • 3 years ago
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    Hello, do you understand how to find the equation of a line?

  2. mjr632
    • 3 years ago
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    y=mx+b

  3. flutterflies
    • 3 years ago
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    so how will the variables fit into the equation?

  4. mjr632
    • 3 years ago
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    Okay, we need two points to find the slope of the linear equation

  5. mjr632
    • 3 years ago
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    Our first point shall be (5, 24.25)

  6. mjr632
    • 3 years ago
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    Can you think of another point that we can intuitively know given the question?

  7. flutterflies
    • 3 years ago
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    (x, 13.5) doesn't give the x value

  8. mjr632
    • 3 years ago
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    Okay, we know how much revenue the company makes when they sell 0 gas, correct?

  9. flutterflies
    • 3 years ago
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    sure.

  10. mjr632
    • 3 years ago
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    How much revenue will they make when they sell 0 gas?

  11. flutterflies
    • 3 years ago
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    wouldn't it just be 0

  12. mjr632
    • 3 years ago
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    Correct

  13. mjr632
    • 3 years ago
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    the equation for the slope of a line is \[m=\frac{y_1-y_2}{x_1-x_2}\]

  14. mjr632
    • 3 years ago
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    We now have two points (0,0) and (5, 24.25)

  15. mjr632
    • 3 years ago
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    Do you see how if we plug in these two points, we can obtain the slope m?

  16. flutterflies
    • 3 years ago
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    slope would be 4.85

  17. mjr632
    • 3 years ago
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    correct

  18. mjr632
    • 3 years ago
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    We know that the equation for a line is y = mx + b

  19. mjr632
    • 3 years ago
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    and we have the value of m

  20. mjr632
    • 3 years ago
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    we also have the value for y and x

  21. mjr632
    • 3 years ago
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    which are (5, 24.25)

  22. mjr632
    • 3 years ago
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    If we plug in these values, m, x and y, then all we have to find is b

  23. flutterflies
    • 3 years ago
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    would the equation be y= 4.85x+48.5?

  24. mjr632
    • 3 years ago
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    no

  25. mjr632
    • 3 years ago
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    24.25 = (4.85)(5)+b

  26. mjr632
    • 3 years ago
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    24.25 = 24.25+b

  27. mjr632
    • 3 years ago
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    Do you see what b must equal?

  28. flutterflies
    • 3 years ago
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    b=0

  29. mjr632
    • 3 years ago
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    Correct

  30. mjr632
    • 3 years ago
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    We now have the full equation

  31. flutterflies
    • 3 years ago
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    equation will be y=4.85x+0

  32. mjr632
    • 3 years ago
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    You got it

  33. mjr632
    • 3 years ago
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    Now you just need to find y = 4.85(13.5)

  34. flutterflies
    • 3 years ago
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    wouldn't the 13.5 be in place of y and not x since the point is (x, 13.5)

  35. mjr632
    • 3 years ago
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    no, the amount of gas is your x variable

  36. mjr632
    • 3 years ago
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    the profit is your y value

  37. flutterflies
    • 3 years ago
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    so the answer would be 65.47

  38. mjr632
    • 3 years ago
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    Correct

  39. flutterflies
    • 3 years ago
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    Thank you!!!!

  40. mjr632
    • 3 years ago
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    You're welcome, good work!

  41. mjr632
    • 3 years ago
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    Did you need any help with any other questions?

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