Math Problem Statement
Solution
Let's analyze the table to determine if there is a proportional relationship between (number of cans) and (cost in dollars).
A proportional relationship occurs when the ratio between and remains constant. In other words, should be the same for all pairs of values.
Let's calculate the ratio for each pair:
- For and , the ratio is .
- For and , the ratio is .
- For and , the ratio is .
- For and , the ratio is .
Since the ratios are not equal, and 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:
- What does a proportional relationship mean in terms of graphing?
- How would you find the constant of proportionality if a relationship were proportional?
- Can you calculate the difference in the cost per can as the number of cans increases?
- What would the equation of a proportional relationship look like?
- 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