1. 1.3 Graphing Data Using Graphs to Get Useful Information from Data

2. Identifying variables  Change only one factor at a time. Ex. If measuring the length of a spring with a weight hanging from it, ONLY change the mass attached. If you change the spring too, you aren’t comparing apples to apples.  Variable – a factor that might affect the behavior of the experimental set-up  Independent Variable – the factor that is changed (In the above ex., mass is the indep var.)  Dependent Variable – the factor that depends on the indep var (ex. Length of the spring)

3. Analyze Data  Line Graph – shows the relationship between the dependent and independent variables.  Line of Best Fit – in science, we don’t draw a line from dot to dot on a graph. We look at all the data points and “eyeball” a line that will come as close to all the data points as possible. It could be a straight line or a curve.

4. Plotting a Line Graph  Take the data table and identify the dependent and independent variables. The independent variable will always be plotted on the x-axis and the dependent variable will always be plotted on the y-axis. Length of Spring for Different Masses Mass attached to spring (g)Length of spring (cm) 013.7 514.1 1014.5 1514.9 2015.3 2515.7 3016.0 3516.4

5. Plotting a Line Graph  Determine range of values for independent variable.  Decide if origin (0,0) is a valid data point.  Spread out data as much as possible. Each line on the graph should be in convenient units.

6. Plotting a Line Graph  Determine range of values for independent variable. independent (the one you change) – mass range = 0-35 g  Decide if origin (0,0) is a valid data point.  Spread out data as much as possible. Each line on the graph should be in convenient units.

7. Plotting a Line Graph  Determine range of values for independent variable. independent (the one you change) – mass range = 0-35 g  Decide if origin (0,0) is a valid data point. Using 0,0 will severely throw off our graph since the range of y values is 13.7-16.4 and we will want to be able to show.5cm increments on the graph.  Spread out data as much as possible. Each line on the graph should be in convenient units.

8. Plotting a Line Graph  Determine range of values for independent variable. independent (the one you change) – mass range = 0-35 g  Decide if origin (0,0) is a valid data point. Using 0,0 will severely throw off our graph since the range of y values is 13.7-16.4 and we will want to be able to show.5cm increments on the graph.  Spread out data as much as possible. Each line on the graph should be in convenient units. 0-35g can be in increments of 1 g Length is from 13.7 to 16.4 cm – intervals of.5cm would show our data but we wouldn’t want to start the y-axis until about 13.0cm to save space, so we use a special symbol.

9. Plotting a Line Graph  Number and Label the horizontal axis. The label should include units. 0 5 10 15 20 25 30 35 40 Mass (g)

10. Plotting a Line Graph  Repeat Steps 2-5 for the dependent variable. 0 5 10 15 20 25 30 35 40 Mass (g) Length (cm) 13.0 13.5 14.0 14.5 15.0 15.5 16.0 16.5 17.0

11. Plotting a Line Graph  Plot your data points. 0 5 10 15 20 25 30 35 40 Mass (g) Length (cm) 13.0 13.5 14.0 14.5 15.0 15.5 16.0 16.5 17.0

12. Plotting a Line Graph  Draw the Line of Best fit.. 0 5 10 15 20 25 30 35 40 Mass (g) Length (cm) 13.0 13.5 14.0 14.5 15.0 15.5 16.0 16.5 17.0

13. Plotting a Line Graph  Name you graph so it describes what you are showing. 0 5 10 15 20 25 30 35 40 Mass (g) Length (cm) 13.0 13.5 14.0 14.5 15.0 15.5 16.0 16.5 17.0 Length of Spring as a Function of Mass

14. What the Graphs Mean  If the Line of Best Fit is a straight line, there is a linear relationship between the two variables.  The equation of a straight line is: y = mx + b slope = my-intercept = b slope = rise run Pick 2 points far apart on the line (they don’t have to be data points) and plug them in: slope = (y 2 – y 1 )y-intercept is point where line (x 2 – x 1 )crosses y-axis (x = 0)

15. What the Graph Means  If your graph is not a straight line, it should be a smooth curve. The two most common types show a quadratic relationship and an inverse relationship between the variables. Time (s) Distance (m) Distance Ball Falls Over Time Current (A) Resistance (Ohms) Current v. Resistance at 120V Quadratic Relationship Inverse Relationship

16. What the Graph Means  Quadratic relationship Formula for the curve is y = ax 2 + bx + c  Inverse Relationship Formula for the curve is y = a/x

17. What the Graph Means  Scientists use these graphs to predict what might happen at values they haven’t tested for. What do you think the car’s position would be at 30 seconds?

18. Graphing Multiple Objects  Say we are tracking two runners in a race and we want to be able to compare their performances. We would graph their position over time on the same graph. Who is running faster? How do you know? 6.0 5.0 4.0 3.0 2.0 1.0 0.00.51.01.52.0 Time (hrs) Position (km) Runner A Runner B

19. Graphing Multiple Objects  Now we are tracking our two runners later in the race. When and where does Runner B pass Runner A? What event occurred at t=0.0s? When Runner A was at 0.0m, where was Runner B? How far apart were the runners at t=10s? 300 250 200 150 100 50 0.0 10203040 Time (s) Position (m) Runner A Runner B -50 50