Question

troy's truck has a 30 gallon gas tank and gets an average of 21 miles per gallon.write an equation to represent the amount of gas in troy' s truck after driving a certain number of miles (assuming he starts with a full tank).define your variables.

Answer 1

Given that Troy's truck has a 30 gallon gas tank and gets an average of 21 miles per gallon.

Let x represent the number of miles Troy's has driven and let y represent the amount of gas in Troy's truck, then the equation that represents the amount of gas, y, in troy' s truck after driving a certain number of miles, x, (assuming he starts with a full tank) is given by

y = 30 - x/21

Answer 2

Let

x---------> represent the number of miles Troy's has driven

y--------> represent the amount of gas in Troy's truck

we know that

the equation that represents the amount of gas, y, in troy' s truck after driving a certain number of miles, x is

`y-y1=m*(x-x1)`

where

m is the slope--------->
`(gallon)/(miles)`

in this problem the slope is equal to
`-(1)/(21) (gallons)/(miles)`

it's negative because the tank is going to be consumed

assuming he starts with a full tank

`for\ x=0\ y=30\ gal`

substitute in the formula above

`y-y1=m*(x-x1)\\\\ y-30=-(1)/(21)*(x-0)\\\\ y=-(x)/(21)+30`

therefore

the answer is

the equation
`y=-(x)/(21)+30`