Math Problem Statement

Is the table proportional or non-proportional?

Solution

To determine if the table is proportional or non-proportional, we need to check if the ratio between corresponding values of xx and yy remains constant. Let's calculate the ratios for each pair of xx and yy:

  1. For x=9x = -9, y=13.5y = 13.5:

    Ratio=yx=13.59=1.5\text{Ratio} = \frac{y}{x} = \frac{13.5}{-9} = -1.5
  2. For x=8x = -8, y=12y = 12:

    Ratio=yx=128=1.5\text{Ratio} = \frac{y}{x} = \frac{12}{-8} = -1.5
  3. For x=7x = -7, y=10.5y = 10.5:

    Ratio=yx=10.57=1.5\text{Ratio} = \frac{y}{x} = \frac{10.5}{-7} = -1.5
  4. For x=6x = -6, y=9y = 9:

    Ratio=yx=96=1.5\text{Ratio} = \frac{y}{x} = \frac{9}{-6} = -1.5

Since the ratio yx\frac{y}{x} is constant for all pairs of xx and yy, the table represents a proportional relationship.

Conclusion:

The table is proportional.


Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:

  1. How can you recognize a proportional relationship in a table?
  2. How do you write the equation of a proportional relationship?
  3. What is the constant of proportionality in this table?
  4. How would the table look if the relationship were non-proportional?
  5. Can you graph the values from the table to verify proportionality?

Tip: A proportional relationship always passes through the origin when graphed.

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Math Problem Analysis

Mathematical Concepts

Proportional Relationships
Ratios

Formulas

Ratio = y/x

Theorems

Proportional Relationships Theorem

Suitable Grade Level

Grades 6-8