Math Problem Statement
Which of the following graphs show a proportional relationship? Choose all answers that apply.
Solution
To determine which graph shows a proportional relationship, let’s review the key characteristics of proportional relationships:
- Proportional relationships must pass through the origin (0, 0).
- They must be linear, meaning they form a straight line.
Analyzing the graphs:
-
Graph A:
- The line does not pass through the origin. It starts at a non-zero point on the y-axis.
- This means it is not proportional.
-
Graph B:
- The line does pass through the origin and is linear.
- This graph shows a proportional relationship.
Correct Answer:
B is the correct answer because it meets the criteria for a proportional relationship.
Would you like additional explanation or further breakdown?
Here are 5 follow-up questions to deepen your understanding:
- What would the equation of the line in a proportional relationship look like?
- Why is passing through the origin critical for proportionality?
- Can a non-linear graph ever be proportional? Why or why not?
- How can you calculate the constant of proportionality from a graph?
- What are some real-world examples of proportional relationships?
Tip: To confirm proportionality, check if the ratio remains constant for all points on the 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
A proportional relationship is linear and passes through the origin (0, 0).
Suitable Grade Level
Grade 7-8