Question

Suppose you start with a full tank of gas (15 gallons) in your truck. After driving 4 hours, you now have 3 gallons left.If x is the number of hours you have been driving, then y is the number of gallons left in the tank.At what rate is your truck using gas? State your answer as a reduced fraction. gallons per hourFind an equation of a line in the form y = mx + b that describes the amount of gas in your tank.y= Submit QuestionQuestion 1

Answer 1

Given:

Amount of gas originally = 15 gallons

Amount of gas after 4 hrs = 3 gallons

x represents the time in hrs

y represents the amount of gas in gallons

The rate at which the truck is using gas can be calculated using the formula:

$\text{Rate = }\frac{Amount\text{ after - Amount before}}{time\text{ duration}}$

Substituting we have:

$\begin{gathered} \text{Rate = }\frac{3\text{ - 15}}{4} \\ =\text{ -}\frac{12}{4} \\ =\text{ -3} \end{gathered}$

The rate at which the truck is using gas is -3 gallons per hr

As a linear equation of the form:

$y\text{ = mx + b}$

where m is the rate at which the truck is using gas and b is the amount of gas originally

Thus:

m = -3

b = 15

Hence, the linear equation that describes the amount of gas is :

$y\text{ = -3x + 15}$

Answer: y = -3x + 15