# Equations (Mathematics Curriculum)

# Linear Equations

## What Is an Equation?

An equation shows us that two things are equal.

An equals sign (=) is used to show that things are equal. What is to the left of the equals sign is equal to what is on the right of the equals sign.

Here is an example of an equation:

The equation above tells us that **x + 1** is equal to **2**.

The quantities on either side are called expressions and can use numbers (**1** and **2**), letters (**x**) and operators (**+**). The equation is expressing a relationship between different numbers and symbols.

### Dictionary Definition

The Oxford English Dictionary defines an equation as "a formula affirming the equivalence of two quantitative expressions, which are for this purpose connected by the sign."

## Robert Recorde and Equations

The first recorded use of the equals sign = in an equation (as well as the plus + and minus − signs in an English book) was by Robert Recorde (1510 - 1558).

It appears in his book 'The Whetstone of Witte':

It is equivalent to '14x + 15 = 71' in today's notation.

He chose two parallel lines of equal length, "bicause noe 2 thynges can be moare equalle."

## What Is a Linear Equation?

A linear equation is a type of equation.

A linear equation has two variables (**x** and **y**). It shows a straight line when plotted on a graph.

Here is an example of a linear equation:

Here is this linear equation plotted on a graph:

## Equations and Linear Equations

Equations show that two mathematical expressions are equal to each other.

Linear equations are the simplest type of equation and show straight lines when plotted.

In this mini-curriculum, you will learn about equations and linear equations.

## Lines, Slope and Y-Intercept

Linear equations can be written in different forms.

The slope-intercept form of a linear equation lets us read off what the slope and y-intercept of a line are.

In this mini-curriculum, you will learn what the slope and y-intercept of a line are and how you can read them off from a linear equation.

## Slope-Point Form

Linear equations can be written in different forms.

The slope-point form of a linear equation lets us read off what the slope of a line is and the Cartesian coordinates of a point the line passes through.

In this mini-curriculum, you will learn about the slope-point form of a linear equation.

## General Form

Linear equations can be written in different forms.

The general form of a linear equation does not let us read off anything about the line it represents.

In this mini-curriculum, you will learn about the general form of a linear equation.

## Equation of a Line Between Two Points

If we know the Cartesian coordinates of two points on a line, the equation of the line can be found.

In this mini-curriculum, you will learn about how to find the linear equation of a line between two points.