Math brings out the artist in you!

While the industrious student can simply whip out a graph calculator to draw up graphing functions, figuring out functions the old-fashioned way can be pretty keen. With nothing but a pencil and a piece of paper divided into little squares, we can create lines and make ‘em dance to the curve of a slope intercept form. Oh yeah, remember that you can hire an online math tutor from Studygate!

We all knew math was a cute little number, but here is where we prove it!

Let’s take a simple equation:

*y = mx + b*

This is a pretty basic format for graphing. We have a Y axis that has a direct relationship with the X axis. The ratio between Y and X is determined by M.

Let’s throw in some numbers and see where they land:

*y = 2x + 6*

This is as easy as it gets. Let’s whip up a graph:

Let’s start easy, with x = 0.

So we know that when X is at 0, Y is 6. The “2” is the ratio between X and Y. If X was 1, then simply multiply *X* *x* 2 + 6 = 8.

We can create a quick chart between X and Y. Don’t forget that we can go into negative values for X and Y s as well!

X | Y |

-4 | -2 |

-3 | 0 |

-2 | 2 |

-1 | 4 |

0 | 6 |

1 | 8 |

2 | 10 |

3 | 12 |

4 | 14 |

5 | 16 |

6 | 18 |

7 | 20 |

Then, plot the points and connect to form a line!

Pretty neat, huh?

****QUICK TIP: go back to the equation

We can break M down to represent the **change over Y over the change over X. **If it were a fraction, it would look like this**: change over Y ÷ change over X
**

Since 2 is basically 2÷1, we can simply say that for every change in X, we move Y up 2 spaces! Look at the chart and do the math. See how it works?

What is M was a **fraction?**It still works out:

This means that for every X value we have, Y goes up by . The chart would look like:

X | Y |

-4 | -1 |

-3 | -.25 |

-2 | .5 |

-1 | 1.25 |

0 | 2 |

1 | 2.75 |

2 | 3.5 |

3 | 4.25 |

4 | 5 |

5 | 5.75 |

6 | 6.5 |

7 | 7.25 |

*Graphs with fraction M look less steep than graphs where M is a whole number.*

* *But where does this get us with **graphing functions?**

**It’s really easy: it’s basically the same thing!**

ƒ(x) = x^{2} + 2

In this case, **Y = F(x).** Since the equation is squared, there will be some curves as the Y intercept changes from positive to negative. But the procedure is the same.

So let’s throw some X values in and see what we get! You can also contact an online math tutor to complete this step.

X | Y |

-5 | 23 |

-4 | 18 |

-3 | 11 |

-2 | 6 |

-1 | 3 |

0 | 2 |

1 | 3 |

2 | 6 |

3 | 11 |

4 | 18 |

5 | 23 |

*As you can see, we have a curve!*

*Imagine the possibilities: with numbers, you can draw anything!*

For more math tips our guide to solving the quadratic formula will help.