Unit B:

Energy Flow in

Technological Systems

The independent variable is also called the manipulated

variable. It is the one that the experimenter changes, or

has control over.

It is always plotted on the horizontal, or x-axis.

When looking at a data table, the independent

variable will be seen to increase by regular

intervals.

The dependent variable is also called the responding

variable. It is the one that the experimenter measures. It’s

value depends on the independent variable. It changes in

response to the change that the experimenter makes to the

manipulated variable.

It is always plotted on the vertical, or y-axis.

When looking at a data table, the

dependent variable will NOT be seen to

increase by regular intervals.

Volume (ml) Mass (g)

10.0 26.7

20.0 53.6

30.0 80.6

40.0 107.1

50.0 134.0

For example, to determine

the density of a liquid, a

student measures the mass

of various volumes of the

liquid.

Volume is the independent

variable because the

experimenter set it, and it

increases by regular

intervals.

Mass is the dependent variable because

the experimenter measured it and it does

not increase by regular intervals.

Mass vs Volume

0

25

50

75

100

125

150

0 10 20 30 40 50 60

Volume (ml)

Mass (

g)

All graphs MUST have

a title, of the y vs x

format.

label

units

label units

Each axis must have the appropriate label

and the symbol (abbreviation) for the units, in brackets.

Slope (m) measures the amount of steepness of a given

line segment.

Slope may be defined as the vertical change (rise) divided

by the horizontal change (run).

slope = m rise

run

y

x

2 1

2 1

y y

x x

Δ = the Greek letter delta

It means “change in . . .”

Distance vs Time

0

20

40

60

80

100

120

0 10 20 30 40 50

Time (h)

Dis

tan

ce (

km

)Pick any two points on the

line.

1 1, 0,0x y

2 2, 30,70x y

Substitute the values

into the slope formula.

2 1

2 1

y yslope

x x

70 0

30 0

km

h

2.3 km/h

Lines with a positive slope rise to the

right.

Lines with a negative slope fall to the

right.

Horizontal lines have a slope of zero.

rise =

run

yslope

x

rise =

run

yslope

x

no vertical change!

Vertical lines have an infinite slope.

∆y = zero

∆x = zero

no horizontal change!

If there is a clear

pattern among the

points, draw a best fit

line that comes as

close as possible to

most of the points.

Best fit line may be

straight or curved. (N)

(m)

read pages 472 - 477

Skill Worksheets 10 & 11