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