To graph the equation \( y = -3x + 2 \), follow these steps:

### 1. Identify the Slope and Y-intercept
The equation is in the slope-intercept form \( y = mx + b \), where:
- \( m = -3 \) is the slope.
- \( b = 2 \) is the y-intercept.

### 2. Plot the Y-intercept
Start by plotting the y-intercept on the graph. The y-intercept is the point where the line crosses the y-axis.
- The point is \( (0, 2) \).

### 3. Use the Slope to Find Another Point
The slope \( -3 \) indicates that for every 1 unit you move to the right (positive direction along the x-axis), you move 3 units down (negative direction along the y-axis).
- From \( (0, 2) \), move 1 unit to the right to \( (1, 2) \), then 3 units down to \( (1, -1) \).

### 4. Plot the Second Point
Plot the second point \( (1, -1) \) on the graph.

### 5. Draw the Line
Draw a straight line through the two points \( (0, 2) \) and \( (1, -1) \). This is the graph of the equation \( y = -3x + 2 \).

If you need the graph drawn, please let me know!

Would you like more details or have any questions?

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Here are some related questions:

1. How would you graph \( y = 2x + 1 \)?
2. What happens to the graph if the slope is positive?
3. How do you find the x-intercept of the equation \( y = -3x + 2 \)?
4. What is the effect of changing the y-intercept on the graph?
5. How would the graph change if the slope were steeper, say \( y = -5x + 2 \)?

**Tip:** The slope determines the steepness and direction of the line, while the y-intercept determines where the line crosses the y-axis.

Learn how to graph the linear equation y = -3x + 2 with this step-by-step guide. Understand the concepts of slope and y-intercept, and plot the graph accurately. Suitable for students in Grades 6-8.

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