Question

Graph the linear equation y = -3x + 2.
What are the plotting points?

Answer 1

To graph the linear equation \( y = -3x + 2 \), we can find several points by substituting different values of \( x \) into the equation. Here are a few points:

1. **When \( x = 0 \)**:
\[
y = -3(0) + 2 = 2 \quad \Rightarrow \quad (0, 2)
\]

2. **When \( x = 1 \)**:
\[
y = -3(1) + 2 = -3 + 2 = -1 \quad \Rightarrow \quad (1, -1)
\]

3. **When \( x = -1 \)**:
\[
y = -3(-1) + 2 = 3 + 2 = 5 \quad \Rightarrow \quad (-1, 5)
\]

4. **When \( x = 2 \)**:
\[
y = -3(2) + 2 = -6 + 2 = -4 \quad \Rightarrow \quad (2, -4)
\]

5. **When \( x = -2 \)**:
\[
y = -3(-2) + 2 = 6 + 2 = 8 \quad \Rightarrow \quad (-2, 8)
\]

### Points to Plot:
- \( (0, 2) \)
- \( (1, -1) \)
- \( (-1, 5) \)
- \( (2, -4) \)
- \( (-2, 8) \)

### Graphing:
To graph the equation, plot these points on a Cartesian plane and draw a straight line through them. The line will have a negative slope (downward from left to right) due to the negative coefficient of \( x \) (-3).

If you were to draw the graph, it would show that as \( x \) increases, \( y \) decreases, following the equation's linearity.