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Teachers & SchoolsStudy Guide

We know that we can graph a linear equation with two variables, such as the famous *x* and *y*, as a straight line. (By the way: that's true only because the variables don't have any exponents, but that's for another day). There are a few special equations that also produce a straight line. Let's look at this one: *y* = 3.

We can graph it by making a table of points.

First we pick a few random values for *x*, like -2, 0 , and 3. Then we plug these numbers into the equation in place of *x*. But waitâ€”there is no *x* variable. No matter what *x* is, *y* will always be 3. Easiest substitution ever.

x-value | y-value | point (x, y) |

-2 | 3 | (-2, 3) |

0 | 3 | (0, 3) |

3 | 3 | (3, 3) |

Now we plot these points on a grid and get a line.

If we pick any point on the line, like the three shown, the *y*-coordinate
will be 3. The *x*-coordinate will vary, but *y* will always be 3.
That's why the equation for this line is *y* = 3.

Take a look at these lines:

Notice anything about all of these horizontal lines? If you answered that they're all *y = something*, then you're right.

**Horizontal lines are all in y = A form, where A is any real number.**

This is because we're graphing all points where *y* equals some number.

Now take a look at these lines:

These dudes are all vertical, and they're in the form *x = something*. Not surprisingly, this is because all points that lie on a vertical line have the same *x*-coordinate.

Here are some points on the line *x* = -1:

See how all the *x*-coordinates equal -1? That's always what happens with vertical lines. **Vertical lines are all in x = B form, where B is any real number.**

If we want to graph the line *y* = -2, all we need to do is plot all the points that have a *y*-coordinate of -2 and connect them, sort of like connect the dots.

We didn't really need to graph *all* of those points. Two would've been sufficient, but we like to make a point (no cheesy math pun intended).