Math Problem Statement
There is 1 in. of water in a pool. The water level is increasing at 0.75 in/min. Which linear equation represents the total depth of the water, in inches, after x minutes?
Solution
The question is asking for the linear equation that represents the total depth of water, in inches, after minutes.
Given:
- Initial water depth = 1 inch.
- Water level is increasing at a rate of 0.75 inches per minute.
This situation can be modeled by the equation of a line: Where:
- is the total water depth after minutes,
- is the rate of increase (slope),
- is the initial water depth (y-intercept).
In this case:
- The rate of increase is inches per minute, so ,
- The initial water depth is 1 inch, so .
Therefore, the equation becomes:
This matches the selected answer, which is correct.
Would you like further clarification on this?
Related Questions:
- How would the equation change if the water level were rising at a different rate?
- What would the equation look like if the pool started with 2 inches of water instead of 1 inch?
- How do you interpret the slope and y-intercept in real-world terms?
- What happens to the water depth if the time is doubled?
- Can you use this equation to find the depth after 10 minutes?
Tip: When interpreting linear equations, always check the initial value (y-intercept) and rate of change (slope) to understand the real-world meaning.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Formulas
y = mx + b
Theorems
Slope-Intercept Form
Suitable Grade Level
Grades 6-8