(6) Notes: Determining Proportionality in Tables, Equations, Graphs

Notes: Determining Proportionality in Tables, Equations, & Graphs Tables: In 1870, the French writer Jules Verne published 20,000 Leagues Under the Sea. One definition of a league is a nut of measure equaling 3 miles. A. Complete the table: Distance (leagues) 1 Distance (miles) 3

2

6

20,000 36

B. What relationships do you see among the numbers in the table?

C. For each column of the table, find the ratio of the distance in miles to the distance in leagues. Write each ratio in simplest form.

3 1

2



6



36 

20,000



Reflection: 1. If you know the distance between two points in leagues, how can you find the distance in miles?

2. If you know the distance between two point in miles, how can you find the distance in leagues?

Ratios, proportions, percents Page 1

Equations: Megan earns $12 an hour at her job. Show the relationship between the amount she earned and the number of hours she worked is a proportional relationship. Then write the equation for the relationship.

Number of hours 1 2 Amount earned $ 12

4

8

Proving proportionality: :

Write an equation: Let

=

=

=

= number of hours Let

=

= the amount earned

Equation =

Try It: Fifteen bicycles are produced each hour at the Speedy Bike Works. Show that the relationship between the number of bikes produced and the number of hours is a proportional relationship. Then write an equation for the relationship.

Ratios, proportions, percents Page 2

Try It: The price of bananas at another store can be determined by the equation: P = $0.35n, where P is the price and n is the number of pounds of bananas. What is the constant of proportionality (unit rate)?

Graphs

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

Use the points on the graph to make a table:

Earth Weight (lb) Moon Weight (lb)

Find the constant of proportionality:

Write an equation: Let = weight on Earth The equation is: Ratios, proportions, percents Page 3

and

= weight on the Moon

The equation is:

Try It: A student is making trail mix. Create a graph to determine if the quantities of nuts and fruit are proportional for each serving size listed in the table. If the quantities are proportional, what is the constant of proportionality or unit rate that defines the relationship? Explain how the constant of proportionality was determined and how it relates to both the table and graph.

Serving Size 1 Cups of Nuts (x) 1 Cups of Fruit (y) 2

2 2 4

3 3 6

Ratios, proportions, percents Page 4

4 4 8

Try It: The graph below represents the cost of gum packs as a unit rate of $2 for every pack of gum. The unit rate is presented as $2/pack. Represent the relationship using a table and an equation.

Ratios, proportions, percents Page 5