Central Dauphin School District



Name: _________________________________________ Date: _________________

Lesson 6-2: Proportional and Nonproportional Relationships

Key Vocabulary:

• Proportional – two quantities are proportional if they have a _________ ratio or rate

• Nonproportional – relationships in which the ratios or rates are _________________.

Proportional Nonproportional

[pic] [pic]

How do I know which number is my x, and which number is my y?

1) x is usually the _______ number in a _________________ table.

2) x is usually the number on the ________ in a _____________ table.

3) x is the _____________ variable, and y is the _______________ variable.

* An independent variable stands alone and is not changed by the other variable.

* A dependent variable depends on the other variable. The independent variable causes a change in the

dependent variable.

Examples:

Determine whether the set of numbers in each of the tables below is proportional.

1) 2)

|Coffee (pounds) |1 |2 |3 |4 |

|Cost (dollars) |3 |6 |9 |12 |

|Time (hours) |1 |2 |3 |4 |

|Distance (miles) |50 |70 |90 |110 |

3) 4)

|Number of Spiders |1 |2 |3 |4 |

|Number of Legs |8 |16 |24 |32 |

5) 6)

|Years |1 |2 |3 |4 |

|Population (100,000) |1.3 |2.1 |3.3 |5.2 |

7) 8)

|Cups of Rice |1 |2 |2.5 |3 |

|Cups of Water |1.5 |3 |3.75 |4.5 |

|Miles Driven |1 |2 |6 |9 |

|Toll Fare |$1.07 |$1.14 |$1.42 |$1.63 |

For each of the following problems, complete the table. Then determine whether the pattern is proportional.

9) Aliya earns $7 per hour babysitting for her neighbors.

10) Antonio’s Pizzeria charges $10 for a large pizza, plus $1.50 for each additional topping.

Key Vocabulary:

• Constant of Proportionality – also called a _______________ or __________________________; in the equation y = kx, which can be used to describe proportional relationships, the constant of proportionality is the variable k.

Examples:

11) A school is repainting some of its classrooms. 12) On a cross-country road trip, a family drives

Each classroom is repainted with 5.5 gallons of 240 miles each day. Write and solve an

paint. Write and solve an equation to determine equation to determine how far the family has

the number of gallons of paint the school must traveled after 4 days.

purchase if they repaint18 classrooms.

What are the two variables?

What is the independent variable? _______________

What is the dependent variable? _________________

13) The circumference of a circle with a diameter of 4 meters is about 12.56 meters. A circle’s circumference

is proportional to its diameter. y x

a. Write an equation relating the circumference of a circle to its diameter.

[pic] Equation: ____________

b. What would be the circumference of a circle with a 6-inch diameter?

14) The cost for 2 ½ pounds of ground beef is $7.20.

a. Write an equation relating cost to the number of pounds of ground beef.

What is the independent variable? _______________

What is the dependent variable? _________________

b. How much is 4 pounds of ground beef?

15) Sue burned 284 calories from walking 4 miles. 16) A store is having a sale where all jeans are

Write an equation relating the number of calories [pic]off the sale price. Write an equation

burned to the number of miles walked. How relating the sale price to the regular price.

many calories would she burn from walking 7 miles? How much would a pair of $35 jeans be on

sale?

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We usually do the ratio [pic], but you can also use [pic].

[pic], which is not equivalent to the other fractions.

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