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The problem asks to write an equation modeling the diver's vertical position \( y \) (in feet) as a function of time \( x \) (in seconds), where the diver descends at a rate of \( \frac{15}{4} \) feet per second.

This is a linear motion problem since the descent is described at a constant rate, which gives a linear relationship between time and depth. The general form of a linear equation is:

\[
y = mx + b
\]

Where:
- \( m \) is the slope (rate of change, or how fast the diver descends),
- \( b \) is the y-intercept (initial position),
- \( x \) is time in seconds, and
- \( y \) is the vertical position in feet.

From the information provided:
- The diver descends at \( \frac{15}{4} \) feet per second, so \( m = -\frac{15}{4} \). The negative sign indicates a downward motion.
- Initially, the diver is at the surface, so at \( x = 0 \), \( y = 0 \). Thus, \( b = 0 \).

The equation becomes:

\[
y = -\frac{15}{4}x
\]

This equation models the diver’s vertical position as they descend over time.

Would you like further details or explanations? Here are five related questions that expand on this topic:

1. How would the equation change if the diver were initially at a depth of 10 feet?
2. How can this situation be modeled using a quadratic equation?
3. What would the diver's position be after 5 seconds?
4. How can you calculate the diver's velocity using this equation?
5. What happens to the graph if the diver ascends instead of descending?

**Tip:** When modeling real-world problems, always pay attention to whether the motion is constant (linear) or changing (quadratic, cubic, etc.).

A snorkeler dives for a shell on a reef. After entering the water, the diver descends 15/4 feet in one second. Write an equation for a parabola that models the diver's vertical position y with respect to time x.

Learn how to model the vertical position of a snorkeler descending into the water using a linear equation. The problem involves calculating the descent rate of 15/4 feet per second and formulating an equation to track the diver's vertical position over time. Suitable for students in grades 8 to 10.

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