One gallon is approximately 3.79 liters. Write a direct variation equation that relates x gallons to y liters.
To write a direct variation equation that relates x gallons to y liters, we need to find the constant of variation.
Since one gallon is approximately 3.79 liters, we can say:
y = kx,
where y is the quantity in liters, x is the quantity in gallons, and k is the constant of variation.
To find k, we can divide both sides of the equation by x:
y/x = k.
Since one gallon is approximately 3.79 liters, we substitute x = 1 and y = 3.79:
3.79/1 = k,
Simplifying, we find:
k = 3.79.
Therefore, the direct variation equation that relates x gallons to y liters is:
y = 3.79x.
To write a direct variation equation, we need to determine the constant of variation. In this case, we know that one gallon is approximately 3.79 liters. This means that the number of liters, y, is directly proportional to the number of gallons, x.
The equation for direct variation is usually written in the form y = kx, where k represents the constant of variation. In this case, to find the value of k, we can use the given conversion between gallons and liters.
We can set up a proportion using the conversion ratio:
1 gallon / 3.79 liters = x gallons / y liters
Simplifying the equation:
1/3.79 = x/y
To eliminate the fraction, we can cross-multiply:
1 * y = 3.79 * x
This gives us the direct variation equation:
y = 3.79x
(3.79 L / 1 gal) is conversion factor
y Liters = x gal * (3.79 L/gal)