1. Year 13 Physics Waimate High School
Graphing and Formulae
Year 13 Physics
Waimate High School

2. Purpose of graphs
Graphs are used to show trends and patterns between information.
Graphs can also be used to make predictions for know situations.
Graphs can be used as a presentation tool.
Graphs can be used to generate a formula that connects variables together.

3. Graphing rules Any graphs must be correctly drawn.
Use error bars where appropriate.
Axes labelled (variable plus units).
Sensible axes scale.
Lines of best fit drawn in.
Titled.
Unless stated, at least 5 data points.
Graphs should be of a reasonable size, at least 1/3 of the page.

4. Graphing errors
This example shows a value of 5.5 ± 0.5 plotted with its error bars.
6.0
5.5
5.0
High error bar
= 6.0
Best estimate of value = 5.5
Low error bar
= 5.0
Error bars can be horizontal, vertical or both for a value.

5. Getting gradients
At this level it is necessary to find the gradient of both the best fit line and the error line.
Remember that gradient is run/rise.
Gradients give you the constant that you need to convert a relationship into a formula.

6. Getting straight line graphs
Sometimes when you draw the initial graph it does not have a straight line for the line of best fit.
The shape of the graph will tell you what transformations need to happen to the raw data to obtain a straight line.
Always transform the independent variable never the dependant variable.

7. Sample graphs and the transformation needed
Parabola
y  x2
Inverse square
y  1/x2
Inverse parabola
y  x

8. Getting a formula from a graph
Once you have a straight line graph it is possible to determine a relationship ie: y axis variable proportional to x axis variable.
The gradient is then used to convert a relationship into a formula ie: y axis variable = gradient x x axis variable + y intercept.

9. Example of getting a formula
Parabola
y  x2 y
Gradient = 2
Y intercept = +5 x2
y  x2
Y= (gradient)x2 + y intercept
Y= 2x2+5

10. Task
Collect the appropriate task sheets and complete your work.