Here are the essential concepts you must grasp in order to answer the question correctly.
Linear Equations
A linear equation is an algebraic expression that represents a straight line when graphed. It typically takes the form y = mx + b, where m is the slope and b is the y-intercept. In this context, the equation y = 52.304x + 396.80 models the relationship between the year and projected sales, allowing us to predict future values based on the linear trend.
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Categorizing Linear Equations
Slope and Intercept
The slope of a linear equation indicates the rate of change of the dependent variable (y) with respect to the independent variable (x). In the given equation, the slope is 52.304, meaning that for each year increase (x), the projected sales increase by approximately 52.304 billion dollars. The y-intercept, 396.80, represents the projected sales when x equals 0, or the year 2016.
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Modeling and Predictions
Modeling in mathematics involves creating a representation of a real-world situation using equations. In this case, the equation models online retail sales over a specific period. By substituting the appropriate value of x (which corresponds to the year 2022, or x=6), we can predict the sales for that year, demonstrating how mathematical models can be used for forecasting in business.
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