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To draw the graph of the equation \( y = 2x - 6 \) for values of \( x \) from \(-2\) to \(5\), we can follow these steps:

### Step-by-Step Solution

1. **Identify the Equation's Type**:
   - The equation \( y = 2x - 6 \) is a linear equation in the slope-intercept form \( y = mx + b \), where:
     - \( m = 2 \) (slope)
     - \( b = -6 \) (y-intercept)

2. **Create a Table of Values**:
   - Substitute values of \( x \) from \(-2\) to \(5\) to find the corresponding \( y \) values.

| \( x \) | \( y = 2x - 6 \) |
|---------|------------------|
| -2      | \( y = 2(-2) - 6 = -10 \) |
| -1      | \( y = 2(-1) - 6 = -8 \)  |
| 0       | \( y = 2(0) - 6 = -6 \)   |
| 1       | \( y = 2(1) - 6 = -4 \)   |
| 2       | \( y = 2(2) - 6 = -2 \)   |
| 3       | \( y = 2(3) - 6 = 0 \)    |
| 4       | \( y = 2(4) - 6 = 2 \)    |
| 5       | \( y = 2(5) - 6 = 4 \)    |

3. **Plot the Points on the Grid**:
   - For each pair \((x, y)\), plot the points \((-2, -10), (-1, -8), (0, -6), (1, -4), (2, -2), (3, 0), (4, 2), (5, 4)\).

4. **Draw the Line**:
   - Connect these points to form a straight line that represents \( y = 2x - 6 \).

### Explanation of the Line
- Since the slope \( m = 2 \), the line rises by 2 units for every increase of 1 unit in \( x \).
- The y-intercept \( b = -6 \) indicates that the line crosses the y-axis at \((0, -6)\).

Would you like me to go through any additional details, or do you have any questions?

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Here are some related questions to extend your understanding:

1. How would the graph change if the slope were negative, say \( y = -2x - 6 \)?
2. What would happen to the line if we changed the y-intercept to a positive number, like \( y = 2x + 3 \)?
3. How can you determine the x-intercept from the equation \( y = 2x - 6 \)?
4. How do you find the slope of a line if only given two points on the line?
5. How can you determine if two lines are parallel or perpendicular just by looking at their equations?

**Tip**: Remember, in linear equations, the slope \( m \) controls the angle of the line, and the y-intercept \( b \) determines where it crosses the y-axis.

On the grid, draw the graph of y = 2x - 6 for values of x from -2 to 5.

Learn how to graph the linear equation y = 2x - 6 for values of x ranging from -2 to 5. This solution includes step-by-step instructions on plotting points, understanding slope and intercept, and drawing the line accurately. Suitable for students in Grades 8-10.

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