Direct Variation• Learn the properties of a direct variation

equation• Graph a direct variation equation• Read a direct variation graph to find missing

values in the corresponding table• Use a direct variation equation to extrapolate

values from a given data set• Develop an intuitive understand of the

concepts of slope and linear equation

Direct VariationPage 114Materials NeededGraph PaperGraphing Calculators

Ship CanalsIn this investigation you will look at data

about canals to draw a graph and write an equation that states the relationship between miles and kilometers. You’ll see several ways of finding the information that is missing from the table.

Complete steps 1 & 2 of the investigation

Ship CanalsCanal Length (Miles) Length (Kilometers)

Albert (Belgium) 80 129Alphonse XIII (Spain) 53 85

Houston (Texas) 50 81Kiel (Germany) 62 99

Main-Danube (Germany) 106 171Moscow-Volga (Russia) 80 129

Panama (Panama) 51 82St. Lawrence Seaway

(Canada/U.S.)189 304

Suez (Egypt) 101Trollhatte (Sweden) 87

Complete step 3 by entering the data in your graphing calculator.

Turn to Calculator Note 1F if you need help entering the data in the graphing calculator.

Complete steps 4 to find the ratio L2:L1. See Calculator Note 1K to create this list. Write your answer to this step on your Communicator®.

Complete step 5 of the investigation. Show how your determined your answer on the Communicator®.

How can you change x miles to y kilometers? Using variables, write an equation to show how miles and kilometers are related.

Use the equation you wrote in the last step to find the length in kilometers of the Suez Canal and the length in miles of the Trollhatte Canal. How is using this equation like using a rate?

Graph the equation on your calculator. Compare this graph to your hand-drawn graph. Why does the graph go through the origin?

Trace the graph of your equation. Approximate the length in kilometers of the Suez Canal by finding when x is approximately 101 miles. Trace the graph to approximate the length in miles of the Trollhatte Canal. How do these answers compare to the one you got from your hand-drawn graph?

Use the calculator’s table to find the missing lengths for the Suez Canal and the Trollhatte Canal.

In this investigation you used several ways to find missing information: Approximating with a graph, calculating with a rate, solving an equation, and searching a table. Write several sentences explaining which of these methods you prefer and why.

Since the ratio was the same for every pair of points, we say that kilometers and miles are directly proportional.

The relationship between kilometers and miles is called a direct variation.

It follows the form y = kx where k is a constant of variation.

Study the example on page 116Use the graphing calculator for parts c and

d Then complete problem 5 on page 118.