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

y=mx+b

so how will the variables fit into the equation?

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

Our first point shall be (5, 24.25)

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

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

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

sure.

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

wouldn't it just be 0

Correct

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

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

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

slope would be 4.85

correct

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

and we have the value of m

we also have the value for y and x

which are (5, 24.25)

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

would the equation be y= 4.85x+48.5?

no

24.25 = (4.85)(5)+b

24.25 = 24.25+b

Do you see what b must equal?

b=0

Correct

We now have the full equation

equation will be y=4.85x+0

You got it

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

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

no, the amount of gas is your x variable

the profit is your y value

so the answer would be 65.47

Correct

Thank you!!!!

You're welcome, good work!

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