Graphing & Interpreting Data Physics 20

Today you will… Graph the relationship between independent and dependent variables Recognize common relationships in graphs Interpret graphs

Graphing Data Data collected during an experiment is recorded in a table where: The first column contains the independent variable (the factor that is deliberately changed). The second column contains the dependent variable (the factor that depends on the independent variable or results of the experiment).

Graphing Data When a graph is made the independent variable is plotted on the x-axis and the dependent variable is plotted on the y-axis.

Graphing Data Good graphs have: each axis labeled with a name, symbol, and unit. each axis with an appropriate scale. data points recorded as a dot, with a small circle around it. a line of best fit drawn a title (usually “y” versus “x”)

Let’s Practice… Turn to Problem Set#1 – do Question 1

Did you…? Label each axis with a name, symbol, and unit? Give each axis with an appropriate scale? Record data points as a dot, with a small circle around it? Draw a line of best fit? Include a title?

Graphical Relationships After data is collected, the graph is then analyzed. There are many graphical relationships that may exist between sets of data. The following are 3 common examples found in physics.

1. Linear Relationship If the line of best fit results in a straight line, there is a linear relationship between the variables. This relationship is indicating that as x changes y changes at the same rate.

1. Linear Relationship The equation for this graph is: Where: m is the slope of the line b is the y intercept

Don’t forget to include units! 1. Linear Relationship Calculating Slope Mathematically, slope provides a measure of the steepness of the line. Don’t forget to include units!

Let’s Practice… Calculate the slope of A and B in your examples!

2. Inverse Relationship When the graph is not a straight line, it means that the relationship between variables is non-linear. One example is an inverse relationship. This means as x increases, y decreases.

2. Inverse Relationship The relationship is stated as y is inversely proportional to x. The equation for this type of graph is y = k/x or y = kx^-1 Where: k=proportionality constant (which is the slope of the graph that is a straight line when the x-data is manipulated)

3. Exponential Relationship Another non-linear relationship is an exponential relationship where as x increases, y increases as a factor of x raised to a power other than 1.

3. Exponential Relationship The relationship is stated as y is proportional to x to the nth power. The equation for this type of graph is: y = kx^n Where: k = the proportionality constant and equals the slope of the straight line graph n can be any power other than 1

Interpreting Graphs Relationships between variables, either in formulas or in graphs, can be used to predict values you have not measured directly.

Interpolation A method of estimating an unknown value that lies between known values

Extrapolation A method of estimating an unknown value that may exist beyond the known values that are plotted on a graph