Since this science course was first examined in 2006 graph questions have become quite common.

There are different types of graph questions, and we will look at each of these different types in turn.

There is nothing scary here, and you have probably covered them all in maths anyway. It’s just that the science textbooks don’t seem to do a very good job of telling us why we have them in the first place, or why there are different types.

**Why do we have graphs?**

You won’t get asked this so you don’t have to learn it off by heart – I just thought you deserved to know.

There are many different reasons, but we’ll just look at two here.

**Reason 1: **

**To see what the relationship is between two variables, e.g. between the extension of a string and the force which caused it.**

Now assuming that a bigger force causes a bigger extension, the question is; are the two quantities directly proportional? i.e. if the size of the force doubles then the extension should be twice as much, if the force triples the extension will be three times as much etc.

Another way of saying this is that the two quantities increase at the same rate (as force is increased the extension increases at the same rate).

**Or finally the scientific way of saying this is to say that ***the two quantities* *are directly proportional to each other* (you must learn the phrase in italics off by heart because it gets asked a lot as you will see below).

To investigate this you would plot the results on a graph, and if the two quantities are directly proportional then you will find that if you draw a line through the points you will end up with a straight line through the origin (the origin is the (0,0) mark).

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**Reason 2: **

**In some graphs the slope of the line gives us some extra information (and you must know what this is).**

There are only three graphs which fall into this category so make sure that you know each of them.

1. The slope of a distance-time graph corresponds to the speed (or velocity) of the moving object

2. The slope of a velocity-time graph corresponds to the acceleration of the moving object

3. The slope of a voltage-current graph corresponds to the resistance of the resistor under investigation.

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**Note that for each of these graphs you will also get a straight line going through the origin, which verifies that the two quantities are directly proportional to each other.**

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**Which brings us to our next problem – how do we calculate the slope of a line?**

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**To calculate the slope of a line**

Pick any two points (from the graph) and label one point (x_{1}y_{1}) and the second point (x_{2}y_{2}).

Make life easy for yourself by picking (0,0) as one of the points (assuming the line goes through the origin).

**You must then use the formula: **

** slope = (y2 – y1)/(x2 – x1)**

**Note that you can also find this formula on page 18 of the new log tables**

**Yo – Which axis is the y-axis?**

Remember the yo-yo? It goes up and down right? Well so does the y axis (and it begins at zero) so y-zero = yo

Now that’s just freaky.