Math Problem Statement

According to the values in the table, do x and y have a proportional relationship?

Solution

Let's analyze the table to determine if there is a proportional relationship between xx (number of cans) and yy (cost in dollars).

A proportional relationship occurs when the ratio between yy and xx remains constant. In other words, yx\frac{y}{x} should be the same for all pairs of values.

Let's calculate the ratio yx\frac{y}{x} for each pair:

  1. For x=11x = 11 and y=24y = 24, the ratio is 24112.18\frac{24}{11} \approx 2.18.
  2. For x=36x = 36 and y=49y = 49, the ratio is 49361.36\frac{49}{36} \approx 1.36.
  3. For x=66x = 66 and y=79y = 79, the ratio is 79661.20\frac{79}{66} \approx 1.20.
  4. For x=85x = 85 and y=98y = 98, the ratio is 98851.15\frac{98}{85} \approx 1.15.

Since the ratios are not equal, xx and yy do not have a proportional relationship.

Would you like more details on proportional relationships, or have any questions about this explanation? Here are five related questions for practice:

  1. What does a proportional relationship mean in terms of graphing?
  2. How would you find the constant of proportionality if a relationship were proportional?
  3. Can you calculate the difference in the cost per can as the number of cans increases?
  4. What would the equation of a proportional relationship look like?
  5. How can you tell if a relationship is linear but not proportional?

Tip: In a proportional relationship, the graph will be a straight line that passes through the origin (0, 0).

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Math Problem Analysis

Mathematical Concepts

Ratios
Proportions
Algebra

Formulas

y = kx (where k is the constant of proportionality)
Ratio: y/x

Theorems

Proportional relationships are characterized by a constant ratio between two variables.

Suitable Grade Level

Grades 6-8