This note tells you what to do when you have finished drawing a graph. (You might also like to have a look at More advanced graph-plotting.)

Use these diagrams and the descriptions in pink to identify the general shape of the graph

 1 A straight line passing through the origin y is directly proportional to x Find the gradient y = m x 2 A straight line not passing through the origin y varies linearly with x Find the gradient and the y-intercept y = m x + c 3 A curve touching neither axis y might be inversely proportional to x Look for a constant product yx y x = constant 4 A curve touching the vertical axis but not touching the horizontal axis y might vary exponentially with x Look for a (constant) half-life y = e -kx  where k = ln2/x½ 5 None of these You could well be reduced to saying "y increases/decreases in a complicated way with x". Click here for hints on coping with non-standard graphs.

In the case of types 1 and 2 you may draw the conclusion indicated in mauve at once with no further ado, substituting the names of the actual quantities plotted vertically and horizontally for the y and x given here.

In the case of types 3 and 4 you must carry out the test indicated in blue first. If it is confirmed, then you may draw the conclusion  indicated in mauve, substituting the names of the actual quantities plotted vertically and horizontally for the y and x given here and removing the 'might'.

It is often the case that the gradient and/or the y-intercept have a physical significance. You should identify this if you can.

(The equation given for type 4 is for men in Senior Part and VI Book only!)