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

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---------> $\frac{gallon}{miles}$

in this problem the slope is equal to $-\frac{1}{21} \frac{gallons}{miles}$

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

$y-y1=m*(x-x1)\\\\ y-30=-\frac{1}{21}*(x-0)\\\\ y=-\frac{x}{21}+30$

therefore

the answer is

the equation $y=-\frac{x}{21}+30$

Answer 2

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