The relationship between any two properties of a system can be represented graphically by a two-dimensional data plot. Such a graph has two axes: a horizontal one corresponding to the independent variable, or the variable whose value is being controlled (*x*), and a vertical axis corresponding to the dependent variable, or the variable whose value is being observed or measured (*y*).

When the value of *y* is changing as a function of *x* (that is, different values of *x* correspond to different values of *y*), a graph of this change can be plotted or sketched. The graph can be produced by using specific values for (*x*,*y*) data pairs.

### Graphing the Dependence of y on x

x | y |
---|---|

1 | 5 |

2 | 10 |

3 | 7 |

4 | 14 |

This table contains the following points: (1,5), (2,10), (3,7), and (4,14). Each of these points can be plotted on a graph and connected to produce a graphical representation of the dependence of y on x.

If the function that describes the dependence of *y* on *x* is known, it may be used to compute x,y data pairs that may subsequently be plotted.

### Plotting Data Pairs

If we know that *y* = *x*^{2} + 2, we can produce a table of a few (*x*,*y*) values and then plot the line based on the data shown here.

x | y = x^{2} + 2 |
---|---|

1 | 3 |

2 | 6 |

3 | 11 |

4 | 18 |

^{2}+ 2