The sales for Best Buy were approximately $35.9 billion in 2006 and $40.0 billion in 2007. Using...

Question:

The sales for Best Buy were approximately $35.9 billion in 2006 and $40.0 billion in 2007.

Using only this information, write a linear equation that gives the sales (in billions of dollars) in terms of the year. Then predict the sales for 2010.

Linear Equation:

We have to predict the sales for 2010. It is an example of linear equation. With the help of the given information we can get two points. Use these points to derived the linear function to get the desired result.

Answer and Explanation:

Let the sales represent on the y-axis and year represent on x-axis. Let 2006 represent x=0. The sales for Best Buy were approximately $35.9 billion in 2006 and $40.0 billion in 2007 which gives us two points {eq}\left( {{x_1},{y_1}} \right) = \left( {0,35.9} \right),\left( {{x_2},{y_2}} \right) = \left( {1,40} \right). {/eq}

Now, find the slope of the sale function with the help of the derived points and we have $$\begin{align*} m &= \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}\\ &= \frac{{40 - 35.9}}{{1 - 0}}\\ m &= 4.1. \end{align*} $$

Use point slope equation to get the linear equation of sale so, we have $$\begin{align*} y - {y_2} &= m\left( {x - {x_2}} \right)\\ y - 40 &= 4.1\left( {x - 1} \right)\\ y &= 4.1x - 4.1 + 40\\ y &= 4.1x + 35.9. \end{align*} $$

For 2010 plug x=4 into the derived linear equation and we have $$\begin{align*} y &= 4.1x + 35.9\\ y &= 4.1\left( 4 \right) + 35.9\\ y &= $52.3 \text{ billion}. \end{align*} $$


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What is a Linear Equation?

from Math 101: College Algebra

Chapter 1 / Lesson 3
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