The equation you provided is in the slope-intercept form \( y = mx + b \), where \( m \) is the slope, and \( b \) is the y-intercept.

Given:
- \( m = -2 \)
- \( b = 2 \)

The equation becomes:
\[
y = -2x + 2
\]

### Steps to solve and graph:
1. **Identify key points**:
   - The y-intercept occurs when \( x = 0 \), so:
     \[
     y = -2(0) + 2 = 2
     \]
     Thus, one point on the graph is \( (0, 2) \).

   - The slope \( m = -2 \) means that for every 1 unit increase in \( x \), \( y \) decreases by 2 units.

2. **Find another point**:
   Choose another value of \( x \), say \( x = 1 \):
   \[
   y = -2(1) + 2 = 0
   \]
   So another point is \( (1, 0) \).

3. **Plot these points**:
   Plot \( (0, 2) \) and \( (1, 0) \) on a graph, and draw a straight line through them, which represents the equation \( y = -2x + 2 \).

I can also graph this for you if you'd like to see the visual. Would you like a graph?

Here are some questions to think about:
1. How do changes in slope affect the steepness of the graph?
2. What would happen if the y-intercept was negative?
3. What is the significance of the slope in real-life applications?
4. How does a vertical shift affect the equation of a line?
5. Can you find the x-intercept of this line?

**Tip**: The slope tells you how fast the line rises or falls, and the y-intercept tells you where it crosses the y-axis.

y = mx + b, m = -2, b = 2. Solve it and graph it.

Explore how to solve and graph the linear equation y = -2x + 2 using slope-intercept form. This problem explains key algebraic concepts like slope, y-intercept, and how to plot lines. Ideal for students in Grades 6-8.

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