At the surface of the ocean, the water pressure is the same...

At the surface of the ocean, the water pressure is the same as the air pressure above the water, 15 Ib/in'. Below the surface, the water pressure increases by 4.34 $\mathrm{lb} / \mathrm{in}^{2}$ for every 10 $\mathrm{ft}$ of descent. $\begin{array}{l}{\text { (a) Express the water pressure as a function of the depth below }} \\ {\text { the ocean surface. }} \\ {\text { (b) At what depth is the pressure } 100 \mathrm{Ib} / \mathrm{in}^{2} ?}\end{array}$

At the surface of the ocean, the water pressure is the same as
the air pressure above the water, 15 Ib/in'. Below the surface,
the water pressure increases by 4.34 $\mathrm{lb} / \mathrm{in}^{2}$ for every 10 $\mathrm{ft}$ of
descent.
$\begin{array}{l}{\text { (a) Express the water pressure as a function of the depth below }} \\ {\text { the ocean surface. }} \\ {\text { (b) At what depth is the pressure } 100 \mathrm{Ib} / \mathrm{in}^{2} ?}\end{array}$

Key Concepts

Linear Functions

Linear functions describe relationships between two quantities where the rate of change is constant. In contexts such as pressure and depth, the relationship is modeled as a straight line, allowing predictions or calculations based on the initial value and a fixed rate of change.

Rate of Change (Slope)

The slope in a linear function represents the rate at which the dependent variable changes with respect to the independent variable. In physical problems, such as the increase of pressure with depth, the slope quantifies how much the pressure increases for each unit of descent, providing critical information about the system's behavior.

Initial Value (Intercept)

The intercept of a linear function is the value of the dependent variable when the independent variable is zero. It often represents a base or starting condition in physical scenarios, such as the pressure at the surface before any additional effects are considered.

Solving Linear Equations

Solving linear equations involves finding the value of the independent variable that results in a specific value of the dependent variable. This process is essential in practical applications where one needs to determine the condition or parameter at which a system reaches a given state.

Units and Dimensional Consistency

Units and dimensional consistency ensure that mathematical expressions involving physical quantities are valid. Correct conversion and matching of units, such as pressure units and depth measures, are crucial for accurate calculations and interpretations in any applied problem.

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