Consider the proportional relationship represented by the equation m=30g, where m is the number of miles traveled and g is the number of gallons of gas used to travel this distance. Describe this relationship.

Answer 1

The equation \( m = 30g \) represents a direct proportional relationship between the number of miles traveled (\( m \)) and the number of gallons of gas used (\( g \)). In this context:

1. Proportionality Constant: The constant of proportionality is 30. This means that for every gallon of gas used, the number of miles traveled increases by 30 miles.

2. Linear Relationship: The relationship is linear, which can be visualized as a straight line when plotted on a graph with \( g \) on the x-axis and \( m \) on the y-axis. The slope of this line is 30, indicating that the distance traveled increases at a consistent rate as more gas is consumed.

3. Intercept: The equation does not have a y-intercept other than 0, indicating that at 0 gallons of gas, no miles can be traveled. This reinforces the idea that this relationship only applies when gasoline is being used.

4. Implications: For practical purposes, this relationship suggests that if a driver uses 1 gallon of gas, they can expect to travel 30 miles; if they use 2 gallons, they will cover 60 miles, and so on. This allows for easy calculations and predictions regarding fuel consumption and travel distance.

Overall, the relationship \( m = 30g \) simplifies the understanding of how fuel efficiency works, specifically indicating that the vehicle can travel 30 miles for every gallon of gas consumed.