You put 14 gallons of gasoline (x) in your car. You know that this amount of gasoline will allow you to drive 420 miles (y). Write and graph an equation to represent the situation.
To represent the relationship between the amount of gasoline (x) and the distance driven (y), we can use the equation:
y = kx
where k is the constant that represents the mileage per gallon.
Given that 14 gallons of gasoline allow you to drive 420 miles:
420 = 14k
We can solve for k by dividing both sides of the equation by 14:
k = 420/14 = 30
Therefore, the equation to represent the situation is:
y = 30x
To graph the equation, we can plot the distance (y) on the vertical axis and the amount of gasoline (x) on the horizontal axis. The slope of the graph will be 30, indicating that for every gallon of gasoline, you can drive 30 miles.
The graph is a straight line passing through the origin.
To write an equation to represent the situation, we need to determine the relationship between the amount of gasoline (x) and the distance driven (y).
Given that 14 gallons of gasoline (x) allows you to drive 420 miles (y), we can conclude that the distance driven is directly proportional to the amount of gasoline.
The equation for direct proportionality is y = kx, where k is the constant of proportionality.
To find the value of k, we can divide the distance driven (y) by the amount of gasoline (x): k = y / x.
Substituting the given values, k = 420 miles / 14 gallons = 30 miles/gallon.
Therefore, the equation to represent the situation is:
y = 30x
To graph this equation, we can plot the amount of gasoline (x) on the x-axis and the distance driven (y) on the y-axis. Each point on the graph will represent a gallon of gasoline and the corresponding distance driven. The graph will be a straight line passing through the origin with a slope of 30.
To write an equation that represents the relationship between the amount of gasoline and the distance traveled, you can use the concept of fuel efficiency. Fuel efficiency is a measure of how far a vehicle can travel on a certain amount of fuel.
In this scenario, you know that 14 gallons of gasoline can allow you to drive 420 miles. So, the fuel efficiency can be calculated by dividing the distance traveled by the amount of gasoline used. Let's denote the fuel efficiency as "e".
Fuel Efficiency (e) = Distance Traveled (y) / Amount of Gasoline (x)
In this case, the fuel efficiency (e) is a constant value since it represents how far you can travel with 1 gallon of gasoline. To find the value of fuel efficiency, we can divide the distance traveled (420 miles) by the amount of gasoline (14 gallons).
e = 420 miles / 14 gallons
e = 30 miles/gallon
Now that we have the fuel efficiency value (30 miles/gallon), we can write the equation:
y = ex
y = 30x
This equation represents the relationship between the amount of gasoline (x) and the distance traveled (y). To graph this equation, you can plot the amount of gasoline on the x-axis and the distance traveled on the y-axis.