Math Problem Statement

Which graph represents a proportional relationship?

Solution

The image you've uploaded contains a set of graphs, each labeled with different variables, representing linear relationships. It appears the question asks you to identify which graph represents a proportional relationship.

Let’s break it down:

  • Proportional relationships are characterized by a constant ratio between the two variables. This means that when you graph the relationship, the line passes through the origin (0,0) and the points along the line have the same constant ratio.

From the graphs:

  • J has a downward sloping line that does not pass through the origin, suggesting it is not proportional.
  • A shows an upward sloping line, which passes through the origin, indicating a proportional relationship.
  • K has a line that passes through the origin and shows a consistent upward slope, which suggests it is also a proportional relationship.

Based on this analysis, A and K are likely proportional relationships.

Would you like further details on this or have any specific questions? Here are some follow-up questions to explore:

  1. How do you determine if a relationship is proportional just by looking at the graph?
  2. What is the formula for a proportional relationship?
  3. How do you calculate the slope of a line in a proportional relationship?
  4. Can proportional relationships be represented by non-linear graphs?
  5. How does the constant of proportionality relate to the slope of the line?

Tip: Always look for the line passing through the origin to quickly spot proportional relationships in a graph!

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Math Problem Analysis

Mathematical Concepts

Proportional Relationships
Linear Graphs

Formulas

y = kx (where k is the constant of proportionality)

Theorems

Proportional Relationship Theorem (lines pass through the origin)

Suitable Grade Level

Grades 6-8