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
[tex] y-y1=m*(x-x1) [/tex]
where
m is the slope---------> [tex] \frac{gallon}{miles} [/tex]
in this problem the slope is equal to [tex] -\frac{1}{21} \frac{gallons}{miles} [/tex]
it's negative because the tank is going to be consumed
assuming he starts with a full tank
[tex] for\ x=0\ y=30\ gal [/tex]
substitute in the formula above
[tex] y-y1=m*(x-x1)\\\\ y-30=-\frac{1}{21}*(x-0)\\\\ y=-\frac{x}{21}+30 [/tex]
therefore
the answer is
the equation [tex] y=-\frac{x}{21}+30 [/tex]
