The graph gives the number of gallons of water in a small...

The graph gives the number of gallons of water in a small swimming pool after $x$ hours. (GRAPHS CANNOT COPY) (a) Write a formula for $f(x)$ (b) Interpret both the slope and the $y$ -intercept. (c) Use the graph to estimate how much water was in the pool after 7 hours. Verify your answer by evaluating $f(x)$

The graph gives the number of gallons of water in a small swimming pool after $x$ hours.
(GRAPHS CANNOT COPY)
(a) Write a formula for $f(x)$
(b) Interpret both the slope and the $y$ -intercept.
(c) Use the graph to estimate how much water was in the pool after 7 hours. Verify your answer by evaluating $f(x)$

Key Concepts

Linear Function

A linear function describes a relationship between two variables with a constant rate of change. It is often written as f(x) = mx + b, where m is the slope and b is the y-intercept. In real-world problems, this form is used to model situations where change occurs steadily over time.

Slope

The slope represents the constant rate at which the dependent variable changes with respect to the independent variable. In applications, it quantifies how much the amount of a quantity (like water) increases or decreases per unit of time. A positive slope indicates an increase, while a negative slope indicates a decrease.

Y-intercept

The y-intercept is the value of the dependent variable when the independent variable is zero. It serves as the starting point for the function, indicating the initial condition of the system being modeled, such as the initial amount of water in a swimming pool.

Function Evaluation

Function evaluation involves substituting a specific value for the independent variable into the function to compute the corresponding value of the dependent variable. This process is useful for predicting or verifying outcomes at particular points, such as finding the amount of water in a pool after a certain number of hours.

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