Getting a Meaningful Relation from a Graph Graphing Getting a Meaningful Relation from a Graph

What do we know already about Graphing??

1. Variables The independent variable: the one that is controlled in order to see how the other variable changes ( on the horizontal axis) Always changes at regular intervals The dependent variable : responds to the changes in the independent variable (vertical axis) May have irregular values (what you are testing for)

Example Experiment: Does increased inhalation of cigarette smoke decrease your lung capacity? What is the independent variable? What is the dependent variable? I.V = Amount of cigarette smoke D.V = Lung capacity Hint – whichever one changes because of the other, is the dependent variable…it depends on the other.

Best Fit Line

Best-Fit Line “Best Fit” lines are used when plotting data on a graph from measurements because: a) measurements involve uncertainty (sig figs!) b) all points on a graph do not necessarily lie on the best fit line that is drawn Thus the name… the line drawn is the ”best fit” you can make to the data given

3. To show the uncertainty associated with each point, we can use: Error bars Error regions (i.e. Regions of Uncertainty) The larger the uncertainty of the measurement, the larger the box.

RULES FOR DRAWING BEST-FIT LINES - Best fit are drawn through a set of points so that: 1) There are as many points above the line as below it This is so that the line isn’t skewed (i.e. averages out) 2) The line should pass through as many regions of uncertainty as possible This is that you “hit” as many points as you can 3) There are as many points on the line as possible- watch (0, 0)! Consider whether a “zero” value for one measure infers a zero measure for the other (e.g. if there is no mass, it would occupy no space!)

Note: If you can draw a straight line through a set of points such that the line passes through all regions of uncertainty, then you are justified in doing so.

Eg. the slope, y-intercept, and the line’s equation Once the best fit line has been drawn, then ALL CALCULATIONS ARE DONE USING POINTS FROM THE LINE! Eg. the slope, y-intercept, and the line’s equation Do NOT use the points or values from your data table!!! NOTE: The best-fit line averages out your errors... Using values that are not on the line/from the equation is BAD!!!

Additional data can be taken from the graph by: Interpolation - using the line to find other values either from the x- or y-axis “Inter”- means within So “inter-polating” means you are finding a value WITHIN your range of points

Interpolation… Is the x value of 5 a data point on the graph? Yes What is the y value for the x value of 5? @ 0.2 Is the x value of 3.5 a data point on the graph? No What is the y value for the x value of 3.5? @ 0.3

Additional data can be taken from the graph by: Extrapolation - extend the line past the last set of points - assume that the trend of the line continues - you can also use the equation of the line to predict values “Extra”- means outside So “extra-polating” means you are finding a value OUTSIDE your range of points

Another method of finding information from a graph(making predictions), is by finding the equation of the line. There are three types of graphs (variations). The following examples will show you how to find the equation for each type of variation and how to identify each one.

Eqn ? 1) Direct Variation - goes through the origin or (0,0) - produces a straight line with a constant slope (m) - general equation is: y= mx Eqn ?

2) Linear Variation - has a “y-intercept” called b (doesn’t got thru 0,0) - produces a straight line - the general equation is: y= mx +b Eqn ?

3) Inverse variations - when one variable increases, the other variable decreases - the general equation is: y= k/x

Eg. : Given the following equation: F= 1.8C + 32 Once you have derived an equation from the graph, then you can make predictions by substituting values into the equation. You must assume, however, that the graph continues in a proportional manner. That is, the slope stays constant. Eg. : Given the following equation: F= 1.8C + 32 1) What is the value of C when F equals 212? 100 2) What is the value of F when C equals -40.0? -40

Work for today: GRAPHING WORKSHEET