Math Problem Statement
Solution
The question asks to find a function that describes the motorboat's distance from the shore based on the given information:
- Initially, the motorboat is 64 km from the shore.
- After 17 minutes, the motorboat is 30 km from the shore.
This setup implies a linear relationship where the motorboat is moving toward the shore, decreasing its distance from the shore over time.
Steps to solve:
-
Slope (rate of change): The motorboat’s speed is constant, meaning the rate of change in distance is linear. We can calculate the slope using the points:
- Initial distance: (0, 64) at time 0 minutes.
- After 17 minutes: (17, 30).
The formula for the slope is:
-
Equation of the line: The general form of a linear equation is: Where:
- (the slope),
- (the initial distance from the shore, i.e., the y-intercept when ).
So, the equation becomes:
Conclusion:
The correct function is Option C: .
Would you like a more detailed explanation or have any other questions?
Here are five related questions you might find useful:
- How do you determine the slope of a line when given two points?
- What is the physical meaning of the slope in this context?
- How do you interpret the y-intercept in real-world linear functions?
- Can a motorboat ever have a positive slope in this scenario?
- How can you verify a linear function using additional data points?
Tip: Always check the units when interpreting real-world linear equations, especially time and distance!
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Formulas
Slope formula: m = (y2 - y1) / (x2 - x1)
Linear equation: y = mx + b
Theorems
Linear function properties
Suitable Grade Level
Grade 8