# Many Students Wonder – Algebra Review (Linear Equation)

## The Algebra of a Line

A line is described by a set of points **(X,Y)** that obey a particular relationship between **X** and **Y**. That relationship is called the equation of the line, which we will express in the following form: **Y = a + bX **In this equation, **a** and **b** are constants that can be either negative or positive. The reason to write the line in this form is that the constants **a** and **b** tell us what the line looks like, as follows:

- The
**intercept (a)**is the value that**Y**takes when**X**= 0 - The
**slope (b)**is the change in**Y**for every increase of 1 unit in**X**.

The slope and intercept are indicated with arrows on the following diagram:

The technique that specifies the dependence of the response variable on the explanatory variable is called **regression**. When that dependence is linear (which is the case in our examples in this section), the technique is called **linear regression**. Linear regression is therefore the technique of finding the line that best fits the pattern of the linear relationship (or in other words, the line that best describes how the response variable linearly depends on the explanatory variable).

To understand how such a line is chosen, consider the following very simplified version of the age-distance example (we left just 6 of the drivers on the scatterplot):

## EXAMPLE:

Consider the line:

The intercept is 1. The slope is 1/3, and the graph of this line is, therefore:

## EXAMPLE:

Consider the line:

The intercept is 1. The slope is -1/3, and the graph of this line is, therefore:

This document is linked from Linear Relationships – Linear Regression.