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flutterflies Group Title

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.

  • one year ago
  • one year ago

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  1. mjr632 Group Title
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    Hello, do you understand how to find the equation of a line?

    • one year ago
  2. mjr632 Group Title
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    y=mx+b

    • one year ago
  3. flutterflies Group Title
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    so how will the variables fit into the equation?

    • one year ago
  4. mjr632 Group Title
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    Okay, we need two points to find the slope of the linear equation

    • one year ago
  5. mjr632 Group Title
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    Our first point shall be (5, 24.25)

    • one year ago
  6. mjr632 Group Title
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    Can you think of another point that we can intuitively know given the question?

    • one year ago
  7. flutterflies Group Title
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    (x, 13.5) doesn't give the x value

    • one year ago
  8. mjr632 Group Title
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    Okay, we know how much revenue the company makes when they sell 0 gas, correct?

    • one year ago
  9. flutterflies Group Title
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    sure.

    • one year ago
  10. mjr632 Group Title
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    How much revenue will they make when they sell 0 gas?

    • one year ago
  11. flutterflies Group Title
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    wouldn't it just be 0

    • one year ago
  12. mjr632 Group Title
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    Correct

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

    • one year ago
  14. mjr632 Group Title
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    We now have two points (0,0) and (5, 24.25)

    • one year ago
  15. mjr632 Group Title
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    Do you see how if we plug in these two points, we can obtain the slope m?

    • one year ago
  16. flutterflies Group Title
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    slope would be 4.85

    • one year ago
  17. mjr632 Group Title
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    correct

    • one year ago
  18. mjr632 Group Title
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    We know that the equation for a line is y = mx + b

    • one year ago
  19. mjr632 Group Title
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    and we have the value of m

    • one year ago
  20. mjr632 Group Title
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    we also have the value for y and x

    • one year ago
  21. mjr632 Group Title
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    which are (5, 24.25)

    • one year ago
  22. mjr632 Group Title
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    If we plug in these values, m, x and y, then all we have to find is b

    • one year ago
  23. flutterflies Group Title
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    would the equation be y= 4.85x+48.5?

    • one year ago
  24. mjr632 Group Title
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    no

    • one year ago
  25. mjr632 Group Title
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    24.25 = (4.85)(5)+b

    • one year ago
  26. mjr632 Group Title
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    24.25 = 24.25+b

    • one year ago
  27. mjr632 Group Title
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    Do you see what b must equal?

    • one year ago
  28. flutterflies Group Title
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    b=0

    • one year ago
  29. mjr632 Group Title
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    Correct

    • one year ago
  30. mjr632 Group Title
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    We now have the full equation

    • one year ago
  31. flutterflies Group Title
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    equation will be y=4.85x+0

    • one year ago
  32. mjr632 Group Title
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    You got it

    • one year ago
  33. mjr632 Group Title
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    Now you just need to find y = 4.85(13.5)

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

    • one year ago
  35. mjr632 Group Title
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    no, the amount of gas is your x variable

    • one year ago
  36. mjr632 Group Title
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    the profit is your y value

    • one year ago
  37. flutterflies Group Title
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    so the answer would be 65.47

    • one year ago
  38. mjr632 Group Title
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    Correct

    • one year ago
  39. flutterflies Group Title
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    Thank you!!!!

    • one year ago
  40. mjr632 Group Title
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    You're welcome, good work!

    • one year ago
  41. mjr632 Group Title
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    Did you need any help with any other questions?

    • one year ago
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