anonymous
  • anonymous
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.
Algebra
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
Hello, do you understand how to find the equation of a line?
anonymous
  • anonymous
y=mx+b
anonymous
  • anonymous
so how will the variables fit into the equation?

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