graphical relationships objectives –learn graphing skills and understand graphical relationships
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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
0
Dis
plac
emen
t (m
)
Time (s)
P (t1, d1)
Q (t2, d2)
t1 t2
d1
d2
Graphical Relationships
Y Does NOT Depend on X (Scatter Diagram)
A = proportional relationshipB = inversely proportional relationshipC = no relationshipD = nonlinear
0 X
Y
Graphical Relationships
A = proportional relationshipB = inversely proportional relationshipC = no relationshipD = nonlinear
0 X
Y
Proportional Relationship
• As X increases, Y increases
• As X decreases, Y decreases
0 X
Y
Graphical Relationships
A = proportional relationshipB = inversely proportional relationshipC = no relationshipD = nonlinear
0 X
Y
Inversely Proportional Relationship
• As X increases, Y decreases
• As X decreases, Y increases
0 X
Y
Graphical Relationships
A = proportional relationshipB = inversely proportional relationshipC = no relationshipD = nonlinear (quadratic or exponential)
0 X
Y
Graphing
• Independent Variable: Experimenter Controls• Dependent Variable: Measurement
• Interval (x-axis) x = x2 - x1
• Interval (y-axis) y = y2 - y1
0
Dep
ende
nt V
aria
ble
IndependentVariable
P (x1, y1)
Q (x2, y2)
x1 x2
y1
y2
y
Graphing
• Slope = rate of change = rise/run = y/x
0
Y
Xx1 x2
y1
y2
y
x
Pathagoras and Right Triangles
c2 = a2 + b2
b
ac
c = hypotenuse = side opposite the right angle
slope = rise/run = a/b
Density
= m/V mass = Volume
0 Volume (cm3)
Mass (grams)Water
IceLead
Density
mass = Volume
Y = slope X
slope is the density, the relationship between
mass and volume, the rate of change of mass
with volume.
0 Volume (cm3)
Mass (grams)Water
IceLead
Density
mass = Volume
A 10 cm3 volume of which substance would weigh the least?
0 Volume (cm3)
Mass (grams)Water
IceLead
Density
mass = Volume
A 5 gram mass of which substance would occupy the
smallest volume?
0 Volume (cm3)
Mass (grams)Water
IceLead