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:

  1. Proportional relationships must pass through the origin (0, 0).
  2. They must be linear, meaning they form a straight line.

Analyzing the graphs:

  1. 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.
  2. 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:

  1. What would the equation of the line in a proportional relationship look like?
  2. Why is passing through the origin critical for proportionality?
  3. Can a non-linear graph ever be proportional? Why or why not?
  4. How can you calculate the constant of proportionality from a graph?
  5. What are some real-world examples of proportional relationships?

Tip: To confirm proportionality, check if the ratio yx\frac{y}{x} remains constant for all points on the graph!

Ask a new question for Free

By Image

Drop file here or Click Here to upload

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