Suppose you want to determine the number of miles you can drive in your car. Your car gets 20 miles per gallon. The number of miles traveled varies directly with the number of gallons of gas the tank holds. Write a direct variation equation that represents this situation... I'm stuck.
m = miles
g = gallons
m = 20g
To write a direct variation equation, we can use the formula:
y = kx
Where:
- y represents the number of miles you can drive (dependent variable)
- x represents the number of gallons of gas in the tank (independent variable)
- k represents the constant of variation
In this case, since the number of miles traveled varies directly with the number of gallons of gas, we can state that when x = 1 (1 gallon of gas), y = 20 (20 miles traveled).
So, we have:
20 = k(1)
To find the value of k, we can divide both sides of the equation by 1:
k(1) = 20 รท 1
k = 20
Therefore, the direct variation equation that represents this situation is:
y = 20x