The image contains a word problem and a linear equation.

Problem:

• You put 13 gallons of gasoline $(x)$ in your car.
• This amount of gasoline allows you to drive 325 miles $(y)$.
• The equation provided is $y = 29x$.

Explanation:

The equation $y = 29x$ represents a linear relationship between the amount of gasoline $x$ and the distance driven $y$. This equation suggests that for every gallon of gasoline, the car can drive 29 miles.

Now, to confirm this relationship:

• Given that $x = 13$ gallons, and you can drive 325 miles,
  • Substitute $x = 13$ into the equation: $y = 29 \times 13 = 377 \text{ miles}$ However, the problem states that 13 gallons allow you to drive 325 miles, but the equation $y = 29x$ predicts 377 miles. This indicates a possible discrepancy between the real-world data and the linear model provided by the equation.

Would you like to explore why this discrepancy might exist or check for alternative interpretations?

Related Questions:

1. How would you correct the equation if the real data shows you drive 325 miles with 13 gallons?
2. What would the fuel efficiency be if you were able to travel 325 miles with 13 gallons?
3. How does the slope of the equation $y = 29x$ affect the relationship between distance and fuel?
4. Can the equation $y = 29x$ be adjusted to better reflect the real-world scenario?
5. How would adding more gallons of gasoline impact your total driving distance using this equation?

Tip:

Always double-check your calculations when dealing with real-world data and models, as slight variations can lead to different outcomes in applications like fuel efficiency.