Review of Graphing – xy plots Why do we graph in science? To see if there is a relationship between 2 variables. 3 most common types of relationships in Physics: Direct (linear) – a change in the value of one variable causes a similar change in the value of the other Ex: amount of $ in paycheck vs hours worked Basic look of graph is a line with a positive slope generic form: y α x where α is the proportional sign Said “y is directly proportional to x”

Inverse – a change in the value of one variable causes an opposite change in the value of the other Ex: price of gas vs how much people drive Basic look of graph is a hyperbola Generic form: y α 1/x Said: “y is proportional to the inverse of x” or “y is inversely proportional to x”

Exponential (power) - as one variable changes value, the other one changes drastically in the same direction Ex: your physics grade vs amount of class/homework you do Basic look of this graph is a parabola generic form is y α x2 Said “y is proportional to x squared”

Where do the numbers for x & y come from? Collected data from an experiment. independent variable – preset values, prior to running the experiment – on x axis dependent – measured against the predetermined values of ind. – on y axis Ex: hours worked & $ in paycheck ind (on x) dep (on y) Ex: amt driven & price of gallon of gas dep (on y) ind (on x)

Standard Form of data chart & graph: data chart : graph: Title: dep vs ind – with more details ind (unit) dep (unit) Be sure to: Decide if (0, 0) should be the first data point – add it to chart and include on graph if yes. Decide best paper orientation, landscape or portrait and Decide appropriate intervals for each axis – must be consistent within each axis – to use entire space provided Provide labels & units on data chart and axes on graph Draw a best fit curve/line of data points – don’t “connect the dots” – looking for 1 of the 3 relationships If a line, determine slope from points on the line – ID points used on the graph – included units