https://file.aiquickdraw.com/mathbot/file/1726195440462kt9x1pai.jpg

The problem asks which of the following can be represented by the equation \( y = 2x \), with the choices being Table A, Graph B, both, or neither.

### Analyzing the options:

1. **Table A**: 
   - The equation given is \( y = 2x \), so for each \( x \) value in the table, \( y \) should be twice the \( x \) value.
   - Checking Table A:
     - When \( x = 2 \), \( y \) is 3. According to \( y = 2x \), \( y \) should be \( 2(2) = 4 \), not 3.
     - When \( x = 4 \), \( y \) is 6. According to \( y = 2x \), \( y \) should be \( 2(4) = 8 \), not 6.
     - When \( x = 6 \), \( y \) is 9. According to \( y = 2x \), \( y \) should be \( 2(6) = 12 \), not 9.
   - Therefore, **Table A** does not represent the equation \( y = 2x \).

2. **Graph B**:
   - The equation \( y = 2x \) represents a straight line with a slope of 2 and a y-intercept of 0.
   - Checking Graph B:
     - The line passes through the origin (0, 0), which fits the equation \( y = 2x \).
     - The slope (rise over run) between points on the line matches a slope of 2. For example, from (0,0) to (1,2), the rise is 2 and the run is 1, which gives a slope of 2.
   - Therefore, **Graph B** represents the equation \( y = 2x \).

### Conclusion:
The correct answer is **B: Graph B only**.

---

Do you want any further details or have any other questions?

Here are some related questions to explore:
1. How do you find the slope of a line given two points?
2. What is the general form of a linear equation?
3. How can you identify the slope and y-intercept from a graph?
4. Can a table of values always represent a linear equation?
5. What does it mean when a table does not follow a linear relationship?

**Tip:** When analyzing tables for linear equations, always check if the changes in \( y \) correspond consistently with the changes in \( x \).

Which of the following can be represented by the equation y = 2x? Options are Table A only, Graph B only, Table A and Graph B, or Neither Table A nor Graph B.

Learn how to determine whether a table of values or a graph can represent the linear equation y = 2x. This problem explores key concepts in algebra, including graphing linear equations and analyzing tables. Suitable for middle school students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation