Graphing Page 4 Physics 30/Kennedy/2015

1.2 Graphical Analysis Page 4 Graphical analysis provides powerful ways of looking at relationships and analyzing data. • All measurements contain some random error (it’s impossible to have a perfect measurement). Some numbers will be lower than they really should be and others will be higher. Drawing a best fit line accounts for this and reduces the effect.   • Consistent errors can be reduced. If a measurement is consistently off, the graph will correct the problem - never force a best fit line to go through zero even though it theoretically should. Physics 30/Kennedy/2015

Graphical Analysis Includes: Page 4 i. Finding an appropriate formula that contains your manipulated and responding variables. ii. Relating your equation to that of a straight line in the form: y = mx + b using the following steps:   • Isolate the responding variable • Set the manipulated variable outside a set of brackets. • Everything left in the brackets comprises the slope of the line. • The y-intercept is represented by the term added or subtracted from the manipulated. Physics 30/Kennedy/2015

Page 6 1. For each of the equations below x is the manipulated variable and y is the responding variable. Place each in slope-intercept form by isolating the responding variable. Complete the chart by identifying the slope and the y-intercept. The first one is done as an example. Equation Slope-intercept form Slope y-intercept a. b. c. d. p. 7 #2 Do Physics 30/Kennedy/2015

However, Page 5 Often the line is not straight. If the line is curved something must be done to make it linear. Physics 30/Kennedy/2015

Memorize (copy on formula sheet) Page 5 Memorize (copy on formula sheet) linear y = mx + b parabolic y = x2 square root y = x inverse inverse square The students must memorize the shapes and formuale. Physics 30/Kennedy/2015

Page 8 3. Use your formula sheet to identify examples of the different types of relationships. State their manipulated and responding variables. [Appendix A] Relationship Example Manipulated variable Responding variable Graph Squared Square root Inverse Inverse square Physics 30/Kennedy/2015

Page 8 4. You are given the task to investigate the relationship between x and y in the formula y = x2. a. Complete the chart to the right. x y x2 1 2 4 3 9 1 4 9 b. Use the data below to construct the graph of y x 1.0 2.0 3.0 4.0 8.0 i. y as a function of x ii. y as a function of x2 x2 12.0 p. 9 #5 Do Physics 30/Kennedy/2015

Identify the manipulated and responding variables Curve Straightening Page 5 Identify the manipulated and responding variables Select a formula that relates the two variables Isolate the responding variable Note what is happening to the manipulated – know your curve shapes. Modify the manipulated variable and replot to get a straight line Anything multiplying and/or dividing the modified manipulated variable is the slope. We will spend about two classes on curve straightening. It will continue to be used throughout the course in order to ensure we better understand it. Memorize your curve shapes! p. 10 #6 Do Physics 30/Kennedy/2015