# Section 2-3

# Graphing Linear Equations

If you have two points, you can draw a straight line connecting them.

So, if you have an equation in two variables and you know that equation is
linear (which means its graph is a line), it’s easy to graph it. All
you need to do is find two ordered pair solutions, plot them, and then draw
the line connecting them. (It’s a good idea to do a third point to check
yourself.)

Example:

Graph the equation *y* = 2*x* + 3.

Start by choosing some easy points for *x*, (say 0, 1, and 2), plug
them in, and calculate the corresponding *y*-values.

*x* |
*y* |

** 0 ** |
** 2(0) + 3 = 3 ** |

** 1 ** |
** 2(1) + 3 = 5 ** |

** 2 ** |
** 2(2) + 3 = 7 ** |

Now, plot the points (0, 3), (1, 5), and (2, 7), and draw the line connecting
them.

Easy!

Sometimes, things can be a little more complicated if the original equation
does not have *y* alone on one side. In this case, you have to solve
for *y* first, and then get your ordered pairs.

**Example: **

Graph the equation **3***y* + 1 = –4*x* + 2*y*.

Start by collecting like terms on one side. Subtract 2*y* from both
sides.

** *** y*** + 1 = –4***x*

Then subtract 1 from both sides.

** *** y*** = –4***x* – 1

Now you can plug in some values of *x* and quickly get the corresponding *y*-values.

## HORIZONTAL AND VERTICAL LINES

Equations of horizontal and vertical lines only have one variable. The equation

** *** x*** = 4 **

represents a vertical line which crosses the *x*-axis at the point
(4, 0). Every ordered pair with 4 as its first coordinate is a solution. (The
equation means “*x* is equal to 4, and *y* can be whatever
it wants.”)

Similarly, the equation

** *** y*** = –3 **

is a horizontal line which crosses the *y*-axis at (0,** –**3).

The point where the horizontal and vertical lines intersect is also easy
to find.