Direct Variation Investigation
The distance that a car travels at 30 miles per hour varies directly with the number of
hours it travels at 30 miles per hour. What does the phrase “varies directly” mean? That
is the concept you will be exploring in this investigation.
You will need the following supplies:
1 – 30 cm ruler
1 – meter stick
1 – tape measure
Select one set of the objects from the supply table (books, cans, locker shelves) and take
it back to your work area.
Fill in the following statement using the words (number & height):
The ________________ of the objects is determined by the ________________ of
objects.
Explain why you filled in the blanks as you did in one or two complete sentences.
There are two variables you considered when you filled in the statement above, height
and number. The first variable is the dependent variable. Its value is dependent upon the
second variable, the independent variable. Label the independent variable and dependent
variable below.
Independent Variable: ______________________________
Dependent Variable: _______________________________
Measure the height of one of the objects to the nearest millimeter and record your
measurement in the table below. In column 1 record the number of objects measured and
in column 2 record the height of the objects. Stack a second item on the first and remeasure. Repeat this process until you have measured the height of all of the objects
stacked. There may be extra slots in the table.
Independent
Dependent
On the grid below, graph the data in the table. Label the x axis with the independent
variable units. Label the y axis with the dependent variable units.
What is the height of zero objects? Graph that point as well.
What do you notice about the shape of your graph?
Return your set of objects to the supply table and select another set of items. Repeat the
measuring and graphing process.
Independent
Dependent
Again, graph the height of zero objects. What do you notice about the shape of your
graph?
If you were to select a third set of objects, predict what the graph would look like. Write
your prediction in the space below.
Refer to the first table you filled in. If you had 10 of those, how tall would a stack of 10
of those be? Explain how you arrived at your answer.
Using y as your dependent variable and x as your independent variable, write an equation
in y = form that describes the data in your first table and graph. Write it in the space
below.
Put your data from your first table in lists 1 & 2 on your calculator. Turn on the scatter
plot function on you calculator and graph it using the zoom 9 function. In Y1 of your
equation editor, graph your y= equation. Describe what you see using one or two
complete sentences.
Did your line go through the points plotted on your calculator? If not, was it close?
Create a table and graph of the situation described at the beginning of this investigation:
The distance that a car travels at 30 miles per hour varies directly with the number of
hours it travels at 30 miles per hour.
What is the independent variable?
What is the dependent variable?
Independent
Dependent
Based upon what you have discovered in this investigation, explain the meaning of the
statement, “The distance that a car travels at 30 miles per hour varies directly with the
number of hours it travels at 30 miles per hour.” Use the information you collected in
both your tables and graphs and the roles of the independent and dependent variables.