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Interpreting graphs

Tutor: Toby

# 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.

$\underline{40\degree C}$​​

## FAQs - Frequently Asked Questions

### How do you read a graph?

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