IB Physics: Chapter 1 Lesson 2b: Graphs

Skills: Plotting graphs. Interpreting graphs. Extracting mathematical relationships from graphs.

Graphs The best way to understand relationships between variables is through plotting graphs. We will always plot “line graphs”. (Never plot bar charts or pie charts…) There are some basic graph plotting rules.

Axes. The Dependent variable always goes on the y-axis. The Independent variable always goes on the x-axis. Label each axis with the variable it represents, make sure you put the units of that variable! Independent variable

Graphs: Axis and Scaling When Choosing how to scale your axes, here are some tips: Always try to use up as much as the paper as possible. Count the number of squares along one axis. Look at the range in your data (ie, what is the largest number you want to plot?) Divide your range by the number of squares. Round up to a sensible number. This will give you how large each square will be worth. Choose a scale that is easy to read (10 is better than 9.5, Other good choices might be 1,2, 2.5, 4, 5, 20, 50 etc…)

Title. Give the graph a good title. The more specific the title, the better.

Draw a best fit line. Plot your points and draw a line of best fit. If the data are obviously falling in a curve, then draw a “best fit curve” (see the graphs on the three previous slides). These data are obviously showing a curve.

Draw a best fit line. If the data fall in what appears to be a straight line, then draw a best fit line using a ruler. Try to have an even spread of data points on either side of the line of best fit (LOBF). If your data have uncertainty bars, try to make the LOBF go through as many uncertainty bars as possible, paying more attention to the smaller uncertainty bars than the larger ones.

Draw a best fit line. WHATEVER YOU DO, NEVER EVER EVER EVER connect the dots. Bad Good

Equation: Straight Line If you are using excel, make sure you display the equation of the line on the graph. Equation of the line

Equation: Straight Line If you are doing the graph (and calculating the slope) by hand, show the points that you are using on the graph by drawing a triangle and showing your slope calculations on the graph. Remember: Choose 2 points on the best fit line Choose them as far apart as you can (usually try to get them at least ½ the length of the line apart from each other) Look for points which the line goes through the “grid line intersections” of the graph paper Use only points from on the line of best fit, NEVER USE DATA POINTS!!! Rise = 230 – 70 Run = 44 – 4

Equation: Straight Line Slope: 𝑠𝑙𝑜𝑝𝑒= 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛 = 230−70 44−4 = 160 40 =4.0 Rise = 230 – 70 Run = 44 – 4

Equation: Straight Line If you are determining the equation by hand, don’t forget your intercept (if one exists) Here the intercept is about 57 (or to be more precise you can calculate it from points on the line and the slope) Rise = 230 – 70 Run = 44 – 4 Intercept

Equation: Straight Line So the final equation is: 𝑦=4.0𝑥+57 Or: 𝑇ℎ𝑖𝑠=4.0𝑡ℎ𝑎𝑡+57