User's Manual
012–07192A Discover Density Set
9
The corresponding graph from table of x
3
and y values is straight, and thus
shows that y is proportional to x
3
. See Figure 4.
x
3
y
edge
3
mass
(cm
3
) (g)
0.5 0.8
2.2 3.3
8.0 12.0
19.7 29.5
50.7 75.9
The analysis has established that y = c x
3
. The constant of proportionality, c, is
simply the slope of the graph. Picking two points (x
1
, y
1
) and (x
2
,y
2
) on the graph
and using the formula for slope
(y
2
- y
1
) / (x
2
- x
1
) gives
c = (90 g - 20 g) / ( 60 cm
3
- 12.5 cm
3
) = 1.47 g/cm
3
Notice that the value for c has dimensional units as part of its value; this will
often be the case in science.
Figure 4
Graph of x
3
vs mass