## An Example of a Linear Equation

An example of a linear equation is shown below: In this example, there are two variables (**x**and

**y**). None of the variables have a number written to the right and above it (that is, the highest exponent is 1).

## Linear Equations as Equations of Lines

The linear equation has two variables:**x**and

**y**. Pairs of values of

**x**and

**y**will make both sides of the equation equal. In the table below, pairs of values of

**x**and

**y**are chosen in the left hand column. They are substituted into the equation (

**y = 2x + 1**) in the right hand column. Both sides of the equals sign are equal.

x = 1, y = 3 | 3 = 2 × 1 + 1 \(\:\:\:\) = 2 + 1 = 3 ✔ |

x = 2, y = 5 | 5 = 2 × 2 + 1 \(\:\:\:\) = 4 + 1 = 5 ✔ |

x = 3, y = 7 | 7 = 2 × 3 + 1 \(\:\:\:\) = 6 + 1 = 7 ✔ |

**x**as the x-coordinate and the value of

**y**as the y-coordinate. These pair of

**x**and

**y**values can be plotted on a graph as Cartesian coordinates

**(x, y)**. When they are plotted, they make a line:

## Forms of Linear Equations

Linear equations come in many forms.- The
*general*form of a linear equation is:

the general form of a linear equation - The
*slope-intercept*form of a linear equation is:**m**is the slope and**c**is the y-intercept.

the slope-intercept form of a linear equation - The
*slope-point*form of a linear equation is:

**m**is the slope of the line, and the point**(x**is a point (in Cartesian coordinates) on the line._{1}, y_{1})

the slope-point form of a linear equation

## What a Linear Equation Is...

Let's see what parts a linear equation can have: A linear equation**can**contain:

- Variables (such as
**y**and**x**above) - Constants (such as
**1**above) - Coefficients - a constant in front of a variable (such as
**2**above)

## ...And What It Isn't

Now let's see what a linear equation cannot have. If you see any of these, it isn't a linear equation. The variables in the linear equation (the**y**and

**x**)

**cannot**contain:

- Exponents - variables can only appear as
**x**and**y**, not as**x**or^{2}**y**^{3} - Roots - variables cannot appear as
**√x**or**∛y**

## Interactive Widget

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