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 xx 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: y=mx+by = mx + b Where:

  • yy is the total water depth after xx minutes,
  • mm is the rate of increase (slope),
  • bb is the initial water depth (y-intercept).

In this case:

  • The rate of increase is 0.750.75 inches per minute, so m=0.75m = 0.75,
  • The initial water depth is 1 inch, so b=1b = 1.

Therefore, the equation becomes: y=0.75x+1y = 0.75x + 1

This matches the selected answer, which is correct.

Would you like further clarification on this?

Related Questions:

  1. How would the equation change if the water level were rising at a different rate?
  2. What would the equation look like if the pool started with 2 inches of water instead of 1 inch?
  3. How do you interpret the slope and y-intercept in real-world terms?
  4. What happens to the water depth if the time xx is doubled?
  5. 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