1. Visualizing Data Section 2.3
Physics

2. Graphing Data First you must analyze your data carefully.
Determine what would be the “best-fit” graph for your needs.
X-axis and Y-axis.
Independent Variable is plotted on Horizontal or X-axis.
Dependent variable is plotted on the Vertical or Y-axis.

3. Determine the range of the independent variable to be plotted.
Decide whether (0,0) is a valid origin point.
Spread the data out. Make each division on your graph stand for a convenient unit.
Number and label the horizontal axis.
Repeat steps for the dependent variable.
Plot the points on the graph.
Draw a best-fit line through the data.
Give the graph a title.

4. Linear Relationships
When a straight line can be drawn through all data points, a LINEAR RELATIONSHIP exists.
The two variables are directly proportional.
Equation for a LINEAR RELATIONSHIP=
y = mx + b

5. Slope The slope is “m” in the equation.
SLOPE: the ratio of vertical change to the horizontal change.
It can also be phrased as the rise over the run.
Or the change in y over the change in x.

6. Y-intercept
The Y-INTERCEPT: “b” is the point at which the line crosses the y-axis, and it is the y-value when the x-value is equal to zero.
When the y-intercept is zero, the equation becomes:
y = mx

7. Linear Graph

8. Non-Linear Relationships
Parabolic Graphs:

9. Parabolic Graphs and Quadratic Equations
Two-variables are related by a QUADRATIC EQUATION:
y = ax2 + bx + c

10. Hyperbolas and Inverse Relationships
INVERSE RELATIONSHIPS: when the dependent variable decreases while the independent variable increases.
Equation:
y = a x
xy = a

11. Questions Time (s) Distance (m) 0.0 0.00 1.0 0.32 2.0 0.60 3.0 0.95
Graph the following:
Draw the best-fit line.
Describe the resulting curve.
What type of relationship is it?
What is the slope of the graph?
Write an equation relating distance and time for the data.
Time (s)
Distance (m)
0.0
0.00
1.0
0.32
2.0
0.60
3.0
0.95
4.0
1.18
5.0
1.45

12. Questions
Explain in your own words the meaning of a steeper line on a line graph.
Equation Notecards.

13. The End