# Junior Cert Science – Graphs and the phrase ‘directly proportional’

Usually there is at least one graph to draw on the Junior Cert Science paper, and if it’s in the Physics section then chances are it will be a straight line graph (the main exception is Cooling Curves). There’s nothing on the syllabus (that I’m aware of) that states that students are expected to know the significance of a straight line graph. In fact here’s a piece of research for you – next time you’re in class ask your students why we’re expected to bother with graphs in the first place. My bet is that very few will be able to give a convincing answer.

One reason we ‘bother’ with graphs is to establish a relationship between two variables; to use the correct jargon we want to see if the variables are ‘directly proportional’ to each other. Now that term ‘directly proportional’ is very important. In means in effect that the two variables are increasing at the same rate. For example if you are on a bicycle travelling at a steady speed of 10 m/s, then for every second that you cycle you will have travelled 10 m (d’oh), and if you travel for twice as long you will cover twice as much ground. If you travel for four and a half times as long, you will cover four and a half times the distance.
So again, the time and the distance covered are increasing at the same rate – they are directly proportional to each other.

The graph is our way of verifying this – it turns out that when you plot all the given data and you end up with a straight line which passes through (0,0) then we can state that the two variables are directly proportional to each other.

So why am I telling you all this now?
Because in the exam you may be asked to draw a graph and then say what the relationship is between the two variables. And if you don’t use the phrase ‘directly proportional’ in your answer then you probably won’t get full marks.
Now as I mentioned I have never seen this phrase highlighted in a Junior Cert textbook so you may well have heard it here first.

Now to help you I have compiled all the graph questions that have ever been asked at Junior Cert into one word document. You can find it on the revision page of thephysicsteacher here (it’s no.3 – Graphs). It also contains all the solutions to the questions, plus a list of do’s and don’ts.

Make sure you check it out before going into the exam. And if you’re reading this as a teacher please remember when photocopying to copy back-to-back and reduce two pages onto one. In doing so you reduce the amount of pages by a factor of 4.

Good luck!