Math Problem Statement
solve
The amount of gas (in gallons) my car has is modeled by the linear function G(d) = -0.2d + 13, where d is the miles traveled since the last time I went to the gas station. Which is an accurate interpretation of the slope?
Solution
The given linear function is:
where represents the amount of gas in gallons, and represents the miles traveled since the last time the car was at the gas station.
Slope interpretation:
- The slope of the equation is , which means that for every additional mile traveled, the amount of gas in the car decreases by 0.2 gallons.
Thus, the accurate interpretation of the slope is:
"We are losing 0.2 gallons of gas every mile."
This corresponds to the third option in the image.
Would you like further details or explanations?
Here are five follow-up questions:
- What is the interpretation of the y-intercept in this equation?
- How do we calculate the total distance traveled before the gas runs out?
- How would the graph of this function look like?
- What is the physical meaning of the slope being negative?
- How can we modify the equation if the fuel efficiency changes?
Tip: The slope in a linear equation like this often represents a rate of change in a real-world context.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Functions
Formulas
y = mx + b (Slope-intercept form)
Theorems
Slope Interpretation
Suitable Grade Level
Grades 6-8