1. What is the slope of (10, 4) and (20,3)?
Graphing Techniques
What is the slope of (10, 4) and (20,3)?

2. Slope Rise over Run y2-y1/x2-x1
What does the slope of a line tell us? The slope tells us the relationship between the variables
Slope can be calculated and found many ways:
Graphs
Data Tables
Equations
Data Points

3. Slope from equation Standard equation for a linear line is: Y=mx+b
Where m = slope
b= y intercept (where the graph crosses the y axis)
Example: y=9x-10
9 is the slope
-10 is the y intercept

4. Equation of a line with Graphs
Y=mx+b
m=slope
b= y intercept
Pick two points that are on the line
Define their coordinates
Example points on this graph: (4,9) and (0,1)
(x,y)
y2-y1/x2-x1
1-9/0-4= -8/-4 = 2= slope
To find the y int it can be done 2 ways
Look to see where the graph crosses the vertical axis
Or plug in numbers in the equation and solve for b
9=2(4) +b
9=8+b
b=1
The equation for this graph is y=2x+1

5. The equation of a line when given data points or a data table
The left column is always the x and the right is always the y
Choose 2 sets of data
(0,15) and (1,20)
Find Slope using y2-y1/x2-x1
20-15/1-0 = 5/1 =5 =slope
To find y intercept plug on set of data into the equation
20=5(1)+b
20=5+b
b=15
Time (s)
Distance (m) 15 1 20 2 25 3 30 4 35
The equation for this data is
Y=5x+15

6. Determining the Variables
The independent is the variable that the experimenter directly changes or varies and is always on the x axis(horizontal axis)
The dependent is the variable that depends on the other variable and is always on the y axis.(vertical axis)
Time is usually always the independent variable. y x

7. Steps for Making a Graph
Identify the independent and dependent variables.
Choose a correct scale you will use. The graph should be large as possible to spread out the data.
Choose a convenient amount of space along the axis. For example, choose every two spaces represent five.
The independent is on the x axis and the dependent variable is on the y axis.
Plot each point with a small dot.

8. Steps Continued Label each axis with the name and its unit.
Title the graph. It should be centered and include the purpose of the graph. For example: Distance vs. Time
If the data points appear to lie roughly in a straight line, draw the best fit line through the dots using a ruler or a straight edge. DO NOT PLAY CONNECT THE DOTS!
If data appears curved make a smooth curved line through as many points as possible.
All graphs do not go through (0,0)
A data table should always accompany the graph.

9. Key Hints
When looking at a data table the independent is always on the left and the dependent is on the right.
Keep it neat as possible.
Always calculate the slope and the equation for the graph if it is linear.
Don’t just write the data points on the x and y axis.

10. Example of a good graph Force (N) Elongation (cm) 0.0 1 1.5 2 3.0 3
0.0 1
1.5 2
3.0 3
4.5 4
6.0

11. Identifying Variables
Time it takes to go a certain distance.
Time is the independent
Distance is the dependent
The speed that you are going at a certain point of time.
How much heat is gained when color is added?
Independent is the color.
Dependent is the heat gained
What happens to the period of a pendulum when mass is added?
Independent is the mass
Dependent is the period of the pendulum