## flutterflies 2 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.

1. mjr632

Hello, do you understand how to find the equation of a line?

2. mjr632

y=mx+b

3. flutterflies

so how will the variables fit into the equation?

4. mjr632

Okay, we need two points to find the slope of the linear equation

5. mjr632

Our first point shall be (5, 24.25)

6. mjr632

Can you think of another point that we can intuitively know given the question?

7. flutterflies

(x, 13.5) doesn't give the x value

8. mjr632

Okay, we know how much revenue the company makes when they sell 0 gas, correct?

9. flutterflies

sure.

10. mjr632

How much revenue will they make when they sell 0 gas?

11. flutterflies

wouldn't it just be 0

12. mjr632

Correct

13. mjr632

the equation for the slope of a line is $m=\frac{y_1-y_2}{x_1-x_2}$

14. mjr632

We now have two points (0,0) and (5, 24.25)

15. mjr632

Do you see how if we plug in these two points, we can obtain the slope m?

16. flutterflies

slope would be 4.85

17. mjr632

correct

18. mjr632

We know that the equation for a line is y = mx + b

19. mjr632

and we have the value of m

20. mjr632

we also have the value for y and x

21. mjr632

which are (5, 24.25)

22. mjr632

If we plug in these values, m, x and y, then all we have to find is b

23. flutterflies

would the equation be y= 4.85x+48.5?

24. mjr632

no

25. mjr632

24.25 = (4.85)(5)+b

26. mjr632

24.25 = 24.25+b

27. mjr632

Do you see what b must equal?

28. flutterflies

b=0

29. mjr632

Correct

30. mjr632

We now have the full equation

31. flutterflies

equation will be y=4.85x+0

32. mjr632

You got it

33. mjr632

Now you just need to find y = 4.85(13.5)

34. flutterflies

wouldn't the 13.5 be in place of y and not x since the point is (x, 13.5)

35. mjr632

no, the amount of gas is your x variable

36. mjr632

the profit is your y value

37. flutterflies

so the answer would be 65.47

38. mjr632

Correct

39. flutterflies

Thank you!!!!

40. mjr632

You're welcome, good work!

41. mjr632

Did you need any help with any other questions?