## anonymous 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.

1. anonymous

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

2. anonymous

y=mx+b

3. anonymous

so how will the variables fit into the equation?

4. anonymous

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

5. anonymous

Our first point shall be (5, 24.25)

6. anonymous

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

7. anonymous

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

8. anonymous

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

9. anonymous

sure.

10. anonymous

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

11. anonymous

wouldn't it just be 0

12. anonymous

Correct

13. anonymous

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

14. anonymous

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

15. anonymous

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

16. anonymous

slope would be 4.85

17. anonymous

correct

18. anonymous

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

19. anonymous

and we have the value of m

20. anonymous

we also have the value for y and x

21. anonymous

which are (5, 24.25)

22. anonymous

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

23. anonymous

would the equation be y= 4.85x+48.5?

24. anonymous

no

25. anonymous

24.25 = (4.85)(5)+b

26. anonymous

24.25 = 24.25+b

27. anonymous

Do you see what b must equal?

28. anonymous

b=0

29. anonymous

Correct

30. anonymous

We now have the full equation

31. anonymous

equation will be y=4.85x+0

32. anonymous

You got it

33. anonymous

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

34. anonymous

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

35. anonymous

no, the amount of gas is your x variable

36. anonymous

the profit is your y value

37. anonymous

so the answer would be 65.47

38. anonymous

Correct

39. anonymous

Thank you!!!!

40. anonymous

You're welcome, good work!

41. anonymous

Did you need any help with any other questions?