Algebraic Representations

• Victoria went to school for x years.

  This is 12 times y, the number of years her brother went to school.

• Victoria spent x dollars to buy a gift for her brother.

  She gave the cashier y dollars and received $12 in charge.

• Victoria has y dollars.

  The amount is 12 times x, the amount of money in dollars Victoria's brother has.

• Victoria is y years old.

  Her age is 12 years greater than x, her brother's age in years.

The tables show the relationships between x and y for two data sets.

Which statement describe the relationships between x and y in Data Set I and Data Set II?

• Both data sets show additive relationships. In Data Set I, y is 5.5 more than x, and Data Set II, y is 5 more than x.

• Data Set I shows a multiplicative relationship in which y is 5.5 times x. Data Set II shows an additive relationship in which y is 20 more than x.

• Both data sets show multiplicative relationships. In Data Set I, y is 5.5 times x, and in Data Set II, y is 5 times x.

• Data Set I shows an additive relationship in which y is 4.5 more than x. Data Set II shows a multiplicative relationship in which y is 5 times x.

The table shows the relationship between r and s, where s is the independent variable.

Which equation represents the relationship between r and s?

Answer explanation

Is there a value being added/subtracted or a value multiplied/divided to the independent variable.

Which equation matches the table?

• y = x + 3

• y = 5x

• y = 2x + 3

• y = 3x + 5

Each small moving box, m, costs $1.25. Which of the following equations best represents the cost, c, of buying m, moving boxes?

• m = 1.25c

• c = m + 1.25

• m = c + 1.25

• c = 1.25m

Which equation best represents the relationship shown in the graph?

• m = 150h

• h = 150m

• m = 75h

• h = 75m

The total number of cookies, y, contained in x packages can be represented by the equation y = 24x. Which of the following graphs best represents this situation?

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Rasco Middle School is organizing a walk-a-thon to raise money to go on a field trip. Students are asking people to pledge $0.10 per lap during the walk-a-thon.

Which equation can be used to describe the table?

• L = 0.10m

• m = 0.10L

• m = 0.10 + L

• L = 0.10 + m

A point representing the location of a library is shown on the coordinate grid. An office is located 4 units away from the library.

Which ordered pair could represent the location of the office?

• (3, 0)

• (0, 4)

• (3, 3)

• (3, 4)

Rasco Middle School is organizing a walk-a-thon to raise money to go on a field trip. Students are asking people to pledge $0.10 per lap during the walk-a-thon. Which of the following statements best describes the table?

• The number of laps is the dependent quantity and the total money pledged is the independent quantity.

• The number of laps and the total money pledged are both independent quantities.

• The number of laps is the independent quantity and the total money pledged is the dependent quantity.

• The number of laps and the total money pledged are both dependent quantities.