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.