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# FUNCTIONS WITH SETS OF DATA: LINEAR MODELING

This guide illustrates how to use an input/output table when given any type of function. In addition, this guide uses formulas and concepts to create models representing a given set of data.

## INTRODUCTION

From business to engineering to cooking to fashion, data is everywhere. Sets of data can inform us about past, present, and future time periods and how those time periods impacted our career or business. Sets of data can be organized into a model, which can better serve you, your employees, and/or a future investor. Creating a linear model from a set of data creates an efficient line of communication that helps people understand what a set of data represents.

## WHAT IS A LINEAR MODEL?

A LINEar model ALWAYS creates a straight line. This straight line can be diagonal, horizontal, or vertical.

How can you remember this? The word "line" is in linear.

## WHAT DOES THE LINEAR MODEL LOOK LIKE? ## HOW TO CALCULATE SLOPE ## FOUR COMPONENTS

There are four components of a linear model:

1. Independent/Input: Any number you plug into a function. These numbers can be used as x-coordinates.
2. Dependent/Output: We can plug any number into a function. After we calculate the function, our answer is our output. These can be used as y-coordinates when graphing.
3. Slope: Slope is the constant change between any two sets of coordinates. Pick any 2 coordinates and subtract the y-coordinates and subtract the x-coordinates. Divide those 2 numbers and that will be your slope.
4. Y-Intercept: Input is ALWAYS 0. Depending on the scenario, this is most likely the starting point.