# Identifying Graphical Relationships(Edexcel International A Level Physics)

Author

Katie M

Expertise

Physics

## Identifying Graphical Relationships

• Graphs are used to visualise the relationship between two sets of data from two different variables
• Common relationships are:
• Directly proportional
• Inversely proportional
• A direct proportionality relationship is where as one amount increases, another amount increases at the same rate
• This is represented by a straight-line graph with a positive gradient
• For two variables, y and x this looks like:

y ∝ x

• An inverse proportionality relationship is where as one amount increases, another amount decreases at the same rate
• This is represented by a curved graph with a decreasing gradient
• For two variables, y and x this looks like:

y ∝

Sketched graphs show relationships between variables

• In the first sketch graph, above you can see that the relationship is a straight line going through the origin
• This means as you double one variable the other variable also doubles so we say the independent variable is directly proportional to the dependent variable
• The second sketched graph shows a shallow curve
• This is the characteristic shape when two variables have an inversely proportional relationship
• The third sketched graph shows a straight horizontal line,
• This means as the independent variable (x-axis) increases the dependent variable does not change or is constant

#### Worked example

Which graph shows the correct relationship between the number of moles of a gas, n, and the temperature, T, at constant pressure and volume?

• The Ideal Gas Equation is PV= nRT
• If P, V and R are constant then  = nT = a constant
• n must be inversely proportional to T
• This is graph D

#### Exam Tip

The best way to know the relationship between two variables is by looking at an equation that links them together, and check that the other variables are constant if one of the variable changes.

Try and use the terms 'directly proportional' or 'inversely proportional' when describing the relationships in exam answer instead of 'as variable x increases then variable y also increases'.

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### Author:Katie M

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.