Chapter 11.2 Graphs are a visual representation of trends in data. Chapter 11 Notes Chapter 11.2 Graphs are a visual representation of trends in data.

Important Terms for this Section Independent variable Dependent variable Best-fit line Extrapolation Interpolation Gradient intercept Inversely proportional Log scales

Plotting graphs Title: should include IV and DV Label axes with quantities and unit Use available space most effectively Use sensible linear scales (no uneven jumps) Plot all points correctly Best-fit line should be smooth (doesn’t have to go through all points) – shows overall trend Identify points that don’t agree with trend Think about whether origin should be included (0,0)

Best-fit lines Does not necessarily pass through any plotted points Can be used to extend the range of measurements (extrapolation) Straight line uses y=mx+c y= dependent variable x= independent variable m= gradient (slope) c= intercept on the vertical axis (y-intercept) Also, m= Δy/Δx

Best-fit lines For a curve, the gradient is the tangent to the curve at that point

Errors and Graphs

Inversely Proportional Sometimes data needs to be processed to produce a straight line Ex: PV are inversely proportional, so P=nRT(1/V) Would look like: Should look like:

Other notes… Graphs without scaled axes = Sketched These show qualitative trends Not for use with experimental data Use excel or other spreadsheet software to plot your graphs! Use the best-fit equation and R2 value to analyze how closely the line fits

Other notes… Be careful that you are using a best-fit that actually demonstrates the trend of the graph