Solve In 2015, Target operated 1792 stores in the United...

Solve In 2015, Target operated 1792 stores in the United States. By 2020, the number of stores had risen to 1897 . Let $y$ be the number of Target stores in the year $x$, where $x=0$ represents 2015. (Source: Target Corporation) a. Write a linear equation that models the number of Target stores in year $x$. b. Use this equation to predict the number of Target stores in 2026.

Solve
In 2015, Target operated 1792 stores in the United States. By 2020, the number of stores had risen to 1897 . Let $y$ be the number of Target stores in the year $x$, where $x=0$ represents 2015. (Source: Target Corporation)
a. Write a linear equation that models the number of Target stores in year $x$.
b. Use this equation to predict the number of Target stores in 2026.

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Key Concepts

Slope-Intercept Form

The slope-intercept form of a linear equation is given by y = mx + b, where m represents the slope (rate of change) and b is the y-intercept (the value of y when x = 0). This form makes it straightforward to understand both the starting value and how changes in x affect y.

Slope Calculation

The slope in a linear model is calculated by dividing the change in the dependent variable by the change in the independent variable over a given interval. This value informs how many units the dependent variable will increase or decrease for each unit increase in the independent variable.

Linear Equations

A linear equation is a mathematical expression that describes a straight-line relationship between two variables. It is used to model relationships where there is a constant rate of change between the variables.

Extrapolation

Extrapolation is the process of using an established linear model to predict values outside the range of the original data. It involves extending the trend line beyond the known data points, assuming that the drawn relationship continues consistently outside that range.

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