Question

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.

Answer 1

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

Answer 2

y=mx+b

Answer 3

so how will the variables fit into the equation?

Answer 4

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

Answer 5

Our first point shall be (5, 24.25)

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

sure.

Answer 10

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

Answer 11

wouldn't it just be 0

Answer 12

Correct

Answer 13

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

Answer 14

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

Answer 15

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

Answer 16

slope would be 4.85

Answer 17

correct

Answer 18

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

Answer 19

and we have the value of m

Answer 20

we also have the value for y and x

Answer 21

which are (5, 24.25)

Answer 22

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

Answer 23

would the equation be y= 4.85x+48.5?

Answer 24

no

Answer 25

24.25 = (4.85)(5)+b

Answer 26

24.25 = 24.25+b

Answer 27

Do you see what b must equal?

Answer 28

b=0

Answer 29

Correct

Answer 30

We now have the full equation

Answer 31

equation will be y=4.85x+0

Answer 32

You got it

Answer 33

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

Answer 34

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

Answer 35

no, the amount of gas is your x variable

Answer 36

the profit is your y value

Answer 37

so the answer would be 65.47

Answer 38

Correct

Answer 39

Thank you!!!!

Answer 40

You're welcome, good work!

Answer 41

Did you need any help with any other questions?