Graphing Linear Equations

**Graphing Linear Equations in Two Variables**

A **linear equation** in two variables is an equation that can be written in the standard form

ax+by=c

where *a*, *b*, and *c* are real numbers

The graphs of the equations *ax* + *by* = *c* are straight lines. This is why the equations are called "linear."

A solution to a linear equation in two variables may be an **ordered pair, ( x, y)**. There may in fact be multiple or infinite possible solutions to a linear equation. For example,

*y = x +*1 has infinite solutions-- (2, 3), (3, 4), (7, 8), to name a few. Since it is not possible to list all the solutions, we instead illustrate them with a

**graph**.

To graph an equation, you will need to determine ordered pairs that satisfy the equation and **plot** the points. It is often helpful to plot at least three points. To determine what points satisfy the equation, you may plug in a number for x and determine the necessary output for y. You may want to rewrite the equation in the form *y = ___* in order to determine the y output more easily. As a final step, draw a line that connects and extends from the three points.

**Example**

Graph the line of

y=x+ 1