https://file.aiquickdraw.com/mathbot/file/1726606939762o5cuoqn7.jpg

Let's analyze the image step by step.

### Part A: Complete the Table
The equation given is \( y = 2x \), which describes a linear relationship. To fill in the table, we can substitute the \( x \)-values into the equation to find the corresponding \( y \)-values.

- When \( x = -2 \): 
  \[
  y = 2(-2) = -4
  \]
- When \( x = -1 \): 
  \[
  y = 2(-1) = -2
  \]
- When \( x = 0 \): 
  \[
  y = 2(0) = 0
  \]
- When \( x = 1 \): 
  \[
  y = 2(1) = 2
  \]
- When \( x = 2 \): 
  \[
  y = 2(2) = 4
  \]

Thus, the completed table looks like this:

| \( x \)  | -2 | -1 | 0  | 1  | 2  |
|---------|----|----|----|----|----|
| \( y \) | -4 | -2 | 0  | 2  | 4  |

The values corresponding to the letters "A" and "B" are:
- \( A = 0 \)
- \( B = 4 \)

### Part B: Similarity and Difference Between the Lines
The two equations are:
- \( y = x \) (red line)
- \( y = 2x \) (blue line)

#### Similarity:
Both lines pass through the origin (0,0), meaning they share the same y-intercept. This means both lines start from the same point on the graph.

#### Difference:
The difference lies in their slopes:
- The slope of the line \( y = x \) is 1.
- The slope of the line \( y = 2x \) is 2.

This means the line \( y = 2x \) is steeper than the line \( y = x \).

Would you like any further details or have additional questions?

Here are some related questions:
1. How do you calculate the slope of a line given two points?
2. How can we determine the y-intercept from an equation?
3. What does the slope tell us about the steepness of a line?
4. How can you graph a line using its slope and y-intercept?
5. How do parallel lines differ from intersecting lines?

**Tip**: When comparing linear equations, always check both the slope and the y-intercept for differences and similarities.

b) The lines y = x and y = 2x are shown on the axis below. Write down one similarity and one difference between these lines.

Compare two linear equations, y = x and y = 2x, by finding one similarity and one difference. Learn about slope and y-intercept, graphing lines, and analyzing linear relationships. Suitable for students in Grades 7-9.

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