CHAPTER 2INVESTIGATION
PROPORTIONAL REASONING / Name______Period ______Date ______
Section 2.4: Direct Variation Investigation
In this investigation you will use data about canals to draw a graph and write an equation to represent the relationship between miles and kilometers. You’ll see several ways to find the information missing from this table.
Step 1Carefully scale these coordinate axes for the data in the table. Let x represent the length in miles and y represent the length in kilometers. Plot points for the first eight coordinate pairs.Step 2What pattern or shape do you see in your graph? Connect the points to illustrate this pattern. Explain how you could use your graph to approximate the length in kilometers of the Suez Canal and the length in miles of the Trollhätte Canal. /
SEE OTHER SIDE
Step 3Calculate the ratio of your two lists to create a new list, . Explain what the values in the third list represent. If you round each value in the third list to the nearest tenth, what do you get?
The number of kilometers is the same in every mile, so the value you found is called a constant.
Step 4Use the rounded value you got in Step 3 to find the length in kilometers of the Suez Canal (to do so, set up a proportion.) Could you also use your result to find the length in miles of the Trollhätte Canal?
Step 5Using the variables x miles and y kilometers, write an equation in the form that shows how miles and kilometers are related.
Step 6Use the equation you wrote in Step 5 to find the length in kilometers of the Suez Canal and the length in miles of the Trollhätte Canal.
Step 7The Canal du Midi in France is 149 miles long. Use your equation from Step 5 or trace the graph to find this length in kilometers.
Step 8The Grand Canal in China is 1746 kilometers long. Find this length in miles, using any method you like.