Graphical Relationships
• Objectives
– Learn graphing skills and understand graphical relationships
Graphing
• What makes a proper Graph?
– A coordinate system
• Origin, defined and labeled
• Data Points, instructions on how they are defined
• Axes, defined, labeled, which way is increasing, units used
Q (t2, d2)
d2
d1
P (t1, d1)
0
t1
t2
Time (s)
Graphical Relationships
Y
0
X
Y Does NOT Depend on X (Scatter Diagram)
A = proportional relationship
B = inversely proportional relationship
C = no relationship
D = nonlinear
Graphical Relationships
Y
0
X
A = proportional relationship
B = inversely proportional relationship
C = no relationship
D = nonlinear
Proportional Relationship
Y
0
• As X increases, Y increases
• As X decreases, Y decreases
X
Graphical Relationships
Y
0
X
A = proportional relationship
B = inversely proportional relationship
C = no relationship
D = nonlinear
Inversely Proportional Relationship
Y
0
• As X increases, Y decreases
• As X decreases, Y increases
X
Graphical Relationships
Y
0
X
A = proportional relationship
B = inversely proportional relationship
C = no relationship
D = nonlinear (quadratic or exponential)
Graphing
Q (x2, y2)
y2
Dy
y1
P (x1, y1)
0
x2 Independent
x1
Variable
• Independent Variable: Experimenter Controls
• Dependent Variable: Measurement
• Interval (x-axis)
• Interval (y-axis)
Dx = x2 - x1
Dy = y2 - y1
Graphing
y2
Dy
y1
0
x1
Dx
x2 X
• Slope = rate of change = rise/run = Dy/Dx
Pathagoras and Right Triangles
c 2 = a2 + b 2
c
a
b
c = hypotenuse = side opposite the right angle
slope = rise/run
= a/b
Density r
Mass (grams)
Lead
Ice
0
r = m/V
Water
Volume (cm3)
mass = r Volume
Density r
Mass (grams)
0
Lead
Water
Ice
Volume (cm3)
mass = r Volume
Y = slope X
slope is the density, the relationship between
mass and volume, the rate of change of mass
with volume.
Density r
Mass (grams)
0
Lead
Water
Ice
Volume (cm3)
mass = r Volume
A 10 cm3 volume of which substance would weigh the
least?
Density r
Mass (grams)
0
Lead
Water
Ice
Volume (cm3)
mass = r Volume
A 5 gram mass of which substance would occupy the
smallest volume?