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.

- anonymous

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- anonymous

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

- anonymous

y=mx+b

- anonymous

so how will the variables fit into the equation?

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- anonymous

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

- anonymous

Our first point shall be (5, 24.25)

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

sure.

- anonymous

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

- anonymous

wouldn't it just be 0

- anonymous

Correct

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

slope would be 4.85

- anonymous

correct

- anonymous

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

- anonymous

and we have the value of m

- anonymous

we also have the value for y and x

- anonymous

which are (5, 24.25)

- anonymous

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

- anonymous

would the equation be y= 4.85x+48.5?

- anonymous

no

- anonymous

24.25 = (4.85)(5)+b

- anonymous

24.25 = 24.25+b

- anonymous

Do you see what b must equal?

- anonymous

b=0

- anonymous

Correct

- anonymous

We now have the full equation

- anonymous

equation will be y=4.85x+0

- anonymous

You got it

- anonymous

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

- anonymous

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

- anonymous

no, the amount of gas is your x variable

- anonymous

the profit is your y value

- anonymous

so the answer would be 65.47

- anonymous

Correct

- anonymous

Thank you!!!!

- anonymous

You're welcome, good work!

- anonymous

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