1. Making a Scientific Graph
The Basics.

2. Identifying Variables
Independent Variable (manipulated variable)
the thing the scientist is changing
gets plotted along the x axis
Dependent Variable (responding variable)
the thing responding to the change
gets plotted on the y axis
Example:
Adding Miracle*Gro to help tomato plants grow taller
Amount of Miracle Gro is Indep Var (Experimenter is directly controlling this)
Height of the plant is the dependent (measuring how this responds )
Write the independent & dependent variable on your paper.

3. Independent & Dependent Variables
Your Turn
Joe wants to see if adding sugar to water will affect the density of the water. He designs an experiment where he measures the density of pure water, then dissolves 5 grams of sugar in and measures the density again. Next, 5 more grams of sugar are added and the density is determined yet again. This is repeated until no more sugar dissolves.
Identify the independent and dependent variable in Joe’s experiment.
Answer: Mass of Sugar (Indep), Density of water (depend).

4. Components of a Graph Axis Labels
Each variable should be clearly labeled with the type of measurement (Mass, Volume, Length, etc)
The units used are put in parenthesis

5. Components of a Graph Title Minimum title: Y vs X
Examples
mass vs volume
Must always include both variables
Better titles are a little more descriptive
The effect of (ind variable) on (dep variable) of (object)
The effect of percentage sugar on density of water
The effect of Mass of Miracle*Gro on the height of tomato plants
“Effect” is the noun, “Affect” is the verb

6. Axis Labels Show example graphs here
Components of a Graph
Title has both variables in it.
Axis Labels
Show example graphs here
Units are in parenthesis after label
Dependent Variable is on Y axis
Independent Variable is on X axis

7. Axis Labels Show example graphs here
Can you find the 6 errors in this graph set-up? Identify as many as you can and then click the numbers at the side to see if you got them all.
Axis Labels
Show example graphs here
Capitals should be used 1
Title only includes one variable
Should be
“affected” 2 3 4
No units are given in parenthesis 5
Variables on wrong axis
Does not describe what was measured 6

8. Example: Properly Set-up Graph

9. Components of a Graph Scale
In a Scientific Graph, the scale is zoomed in so that the graph “fills the paper”
to set scale, look at the range of your data for each variable
Put lowest value near bottom edge of graph and highest value near top
This span should cover at least 75% of graph
Scale does not have to start at 0,0
Try to make every block equal to a “nice” number
1,2,4,5 or any division of 10 of these (0.2, .05, 400. etc)
Stay away from ‘ugly’ scales
Every block = 3,7,9, etc

10. Identifying Variables - Example
Let’s say we were making a graph of the relationship the between the temperature and the volume of a balloon. If we did this by changing the temperature and recording what the consequent volume was, then the __________ would be the independent variable, and the ___________ would be the dependent variable.
temperature
volume

11. What axis does the independent variable go on?
What is the dependent variable?
How do we show the units?
What would be a good title?
Notice how it fills the window & does not start at zero

12. Example of Poor X Axis Scale:
Empty Space !!!!!

13. Example of Poor Y Axis Scale:
Empty Space !!!!!

14. Example of Poor Y Axis Scale:
Fills up less than half of window

15. Don’t actually need to do, but think about how you would set it up
Set an appropriate scale for the data below and plot the points on your graph paper
Trial
Mass of Miracle Gro
(grams)
Height of plant
(cm) 1
11.7 2
14.0 3 4
15.6 6
18.6 5 8
19.6
Fill out scale legend at top of graph paper
Don’t actually need to do, but think about how you would set it up

16. Your Turn: Appropriate Scales
Notice Scale does not start at 0,0.

17. Best-Fit Line
Once points are plotted, draw the straight line that comes closest to hitting all points.

18. Best-Fit Line
Notice that about half the points are above line and half are below. The line represents the ‘middle’ of all of the points.
Above Line
Below Line

19. Another Example of a best-fit line
Another Example of a best-fit line. Notice that the line does not actually hit any of the data points.

20. How do you find the slope of a line?
Slope is the rise over the run.
Slope = ΔY ΔX
Slope = Y2 – Y1
X2 – X1

21. Determining the Slope of a Best-Fit Line
Pick any two points that are on your best-fit line
Pick points that are fairly far apart
These two points are
NOT on your line
They will give you the
slope of a different line
instead of your
best-fit line

22. Determining the Slope of a Best-Fit Line
Write the coordinates for those 2 points on your graph
Use the coordinates to calculate the slope of best-fit line
(36.8, 2.50)
Slope = Y2 – Y1
X2 – X1
Slope = L – 1.50L
36.8 C – 20.0 C
(20.0, 1.50)
Slope = L/°C

23. Interpolating Data Volume = 1.91 L
Use the graph to predict what is the volume of the balloon at 27 deg C ?
Volume = 1.91 L

24. Interpolating Data Temp = 38.0 °C
At what temperature is the balloon 2.5 liters ?
Temp = 38.0 °C

25. Interpolating Data Temp = 38.0 °C
What would the volume of the balloon be at 80 C ?
Temp = 38.0 °C

26. solve this without using graph?
Extrapolating Data
What is the volume of the balloon when it is 80 °C?
Volume = 4.8 L
Can you think of a way to
solve this without using graph?
Interpolating Range

27. Predicted value is outside of range of tested values
Extrapolating Data
What is the volume of the balloon when it is 80 °C?
Volume = 4.8 L
Predicted value is outside of range of tested values
Interpolating
Range

28. Explain the difference between interpolating and extrapolating from your data. Compare the reliability of the two.

29. Your Turn: Determine the Slope of the Line

30. Your Turn: Determine the Slope of the Line
General formula for any
straight line
How does this slope compare with yours?
Same Answer?
Sig Figs?
Units?

31. Your Turn: Determine the Slope of the Line
m = slope
b = Y-intercept:
Value of Y when x = 0
More on Y-intercept
Equation can be made more specific:
Y = m x b
= ( ) +
Height
1.02 cm/g
Mass
11.8cm

32. Which equation represents the following graph correctly?
A. volume = -3g/mL (mass) + 6
B. mass = 2g/mL (volume) -3
Volume (mL)
C. -3 = 6g/mL (volume) + mass
D. volume = 2g/mL (mass) + 6
E. mass = 2g/mL (volume) + -3
Mass (g)

33. Which equation represents the following graph correctly?
Volume is Dependent
Variable
( on Y axis)
Volume (mL)
D. volume = 2g/mL (mass) + 6
Mass is Independent
Variable
( on X axis)
y = m (x) b
Mass (g)

34. Sketch a graph represented by
Speed = -5mps/m (Height) + 25
Y intercept = 25
Slope = -5 mps/m
Speed is Dependent
Variable
( on Y axis)
Height is Independent
Variable
( on X axis)

35. Sketch a graph represented by
Speed = -5mps/m (Height) + 25
What will the speed be
when the height is 3 m?
Can Interpolate or plug
values into equation

36. Warm-Up: Write a specific equation for the line below
(1.0,20.0)
(2.0,15.0)
Speed (m/s)
(3.0,10.0)
(4.0,5.0)

37. Sketch a graph represented by
Speed = -5mps/m (Height) + 25
Y intercept = 25
Slope = -5 mps/m
Speed is Dependent
Variable
( on Y axis)
Height is Independent
Variable
( on X axis)

38. The End

39. Y- Intercept
What is the Y-Intercept of this graph ?
Y intercept = 2

40. Y- Intercept Y intercept = 11.8 cm
What is the Y-Intercept of this graph ?
Y intercept = 11.8 cm

41. What is the Y- Intercept?
Why isn’t this the Y-Intercept?

42. What is the Y- Intercept?
Back
Y-Intercept = 0