Water Flow The graph gives the number of gallons of water in...

Water Flow The graph gives the number of gallons of water in a small swimming pool after $x$ hours. (graph can't 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 $f(x)$

Water Flow The graph gives the number of gallons of water in a small swimming pool after $x$ hours.
(graph can't 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 $f(x)$

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Key Concepts

Graphical Interpretation

Graphical interpretation involves reading a graph to extract meaningful information such as values at specific points, trends, and rates of change. This step is crucial for converting visual data into a mathematical model, allowing one to formulate equations and make predictions based on the graph.

Y-Intercept

The y-intercept is the value of the function when the independent variable is zero, serving as the starting point of the measurement. For example, it indicates the initial amount of water present before any changes began to occur.

Linear Functions

A linear function is represented by the equation f(x) = mx + b, where m is the slope and b is the y-intercept. This type of function characterizes a constant rate of change between the independent variable (often time or another permitting quantity) and the dependent variable (such as a measurement of water level).

Slope

The slope represents the rate of change of the dependent variable with respect to the independent variable. In contexts involving water flow, the slope tells us how many gallons of water are added or removed per hour, indicating whether the water is increasing or decreasing over time.

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