# Interpreting graphs

## In a nutshell

Graphs allow information to be displayed in a way such that it is easier to digest and understand. Coordinate grids with two axes, for example $x$- and $y$-axes, allow quick connections to be made between two sets of information. By using one coordinate, the other coordinate can be located by reading off the graph.

## Coordinates reminder

When reading coordinates, you read the $x$-coordinate first, then the $y$-coordinate. The $x$-coordinate shows how far left or right a point is and the $y$-coordinate shows how far up or down a point is.

##### Example 1

$(5,8)$* has *$x$*-coordinate *$5$* and *$y$*-coordinate *$8$*. *

*The *$x$*-coordinate is *$5$* places to the right of the origin, as it is positive.*

*The *$y$*-coordinate is *$8$* places up from the origin, as it is positive.*

## Real-life graphs

Graphs are used to depict information, so are used in all sorts of real-life scenarios: for example tracking temperature against time, or distance against speed. Hence, being able to read a graph is crucial to their utility.

#### procedure

**1.** | Each point on a line or curve on a graph will have a pair of coordinates (usually $x$ and $y$, but they can essentially be any letters). Locate the point you are interested in. |

**2.** | Read off its $x$-coordinate (by looking at the horizontal axis and seeing which value on it the point is in-line with). |

**3.**
| Read off its $y$-coordinate (by looking at the vertical axis and seeing which value on it the point is in-line with). |

**4.**
| You now have the coordinates of the point and can hence relate two pieces of information: the $x$-value with the $y$-value. |

##### Example 2

*The graph below shows the relationship between time passed ($t$) and the temperature ($T$) of a cup of coffee in $\degree C$. **What is the temperature of the coffee $4$ minutes after it is made?*

*Firstly, look along the time ($t$) axis (horizontally) at** $4$ minutes. *

*Move up until you meet the line of the graph. *

*Finally, move across to read the temperature on the $T$*-axis. * *

*$\underline{40\degree C}$*