REPRESENTING PROPORTIONAL RELATIONSHIPS WITH GRAPHS

Example 1 :

The graph shows the relationship between the weight of an object on the Moon and its weight on Earth. Write an equation for this relationship.

Solution :

Step 1 :

Make a table relating the weight of the object on the Moon to its weight on Earth.

Step 2 :

Find the constant of proportionality.

Moon weight : Earth weight

1 : 6 = 1  : 6

2 : 12 = 1  : 6

3 : 18 = 1  : 6

5 : 30 = 1  : 6

The constant of proportionality is 1 : 6 or 1/6.

Step 3 :

Write an equation.

Let x represent weight on Earth.

Let y represent weight on the Moon.

The equation is y = kx.

Replace k with 1/6 in the above equation.

y = (1/6)x

y = x/6

Example 2 :

In 1870, the French writer Jules Verne published 20,000 Leagues Under the Sea, one of the most popular science fiction novels ever written. The graph shows the relationship between the distance in leagues and distance in miles. Write an equation for this relationship.

Solution :

Step 1 :

Make a table relating distance in leagues and distance in miles.

Step 2 :

Find the constant of proportionality.

Miles : Leagues

3 : 1 = 3 : 1

6 : 2 = 3 : 1

18 : 6 = 3 : 1

36 : 12 = 3 : 1

60,000 : 20,000 = 3 : 1

The constant of proportionality is 3 : 1 or 3/1 or 3.

Step 3 :

Write an equation.

Let x represent the distance in leagues.

Let y represent the distance in miles.

The equation is y = kx.

Replace k with 3 in the above equation.

y = 3x

Example 3 :

The graph shows the relationship between the amount of time that a backpacker hikes and the distance traveled.  Write an equation for this relationship.

Solution :

Step 1 :

Make a table relating distance and time.

Step 2 :

Find the constant of proportionality.

Distance : Time

6 : 5 = 6 : 5

12 : 10 = 6 : 5

18 : 15 = 6 : 5

The constant of proportionality is 6 : 5 or 6/5.

Step 3 :

Write an equation.

Let x represent time in hours.

Let y represent the distance in miles.

The equation is y = kx.

Replace k with 6/5 in the above equation.

y = (6/5)x

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