# Math 10 question? Please anyone know?

Jana filled up the gas tank of 58L and drove the vehicle until it was empty. She drove the SUV for 464km.

Write an equation in slope-intercept from which represents the volume of the fuel in the tank. V as a function of distance d.

Determine the distance traveled when 12 L of gas is left

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• At 0km she had 58𝑙 (0,58) and at 464km she had 0𝑙 (464,0)

V/58 + d/464 = 1 so V(d) = -1/8 d + 58

d(V) = 464 - 8V so when 12𝑙 remain Jana has traveled 464 - 8*12 = 368km

(and has 8*12 = 96km to empty the tank)

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• If Jana is driving the vehicle at a constant speed, it volume of gas that it burns each mile will be constant. To determine this number, use the following equation.

V = k * d

58 = k * 464

k = 58 ÷ 464 = 0.125 L/km or ⅛ L/km

Determine the distance traveled when 12 L of gas is left

V = 58 – 12 = 46

46 = 0.125 * d

d = 368 km

I hope this is helpful for you.

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• Hint:

(V=58 , d= 0 )

(V=0 , d= 464 )

write an equation with given points

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• i) Consumption = 58L/464km = 1/8 L/km

V = 58 - d/8

ii) 12 = 58 - d/8

d = 368 km

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• With d = 0, the tank is 58L, so we have one data point: (0, 58)

Then after 464 km, the tank is empty, so this data point is: (464, 0)

To get the equation between the points we need to find the slope first which is the change in y over the change in x:

m = (58 - 0) / (0 - 464)

m = 58 / (-464)

m = -1/8

Then we have the intercept already from the first data point:

b = 58

So the equation is:

V = (-1/8)d + 58

For the volume of gas remaining after "d" km has been driven.

What's the distance traveled with 12 L of gas remains? Solve for d when V = 12:

12 = (-1/8)d + 58

-46 = (-1/8)d

46(8) = d

d = 368 km

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