Question
Graph the linear equation y = -3x + 2.
What are the plotting ?
What are the plotting ?
Answers
GPT-4o mini
To graph the linear equation \( y = -3x + 2 \), you can follow these steps:
1. **Identify the slope and the y-intercept**:
- The slope \( m \) is -3, which means for every 1 unit increase in \( x \), \( y \) decreases by 3 units.
- The y-intercept \( b \) is 2, which means the graph crosses the y-axis at the point (0, 2).
2. **Plot the y-intercept**:
- Start by plotting the point (0, 2) on the graph.
3. **Use the slope to find another point**:
- From the point (0, 2), apply the slope. Since the slope is -3, you can move down 3 units and 1 unit to the right:
1. From (0, 2), move down to 2 - 3 = -1, and move right to 1. This gives you the point (1, -1).
4. **Plot the second point**:
- Plot the point (1, -1) on the graph.
5. **Draw the line**:
- Draw a straight line through the points (0, 2) and (1, -1). Extend this line in both directions and add arrows at each end to indicate that it continues infinitely.
6. **Calculate additional points (optional)**:
- You could calculate more points by choosing different values for \( x \), substituting them into the equation \( y = -3x + 2 \), and plotting those points:
- For \( x = -1 \): \( y = -3(-1) + 2 = 5 \) → point (-1, 5)
- For \( x = 2 \): \( y = -3(2) + 2 = -4 \) → point (2, -4)
By following these steps, you will have a proper graph of the linear equation \( y = -3x + 2 \). The graph will slope downwards from left to right due to the negative slope.
1. **Identify the slope and the y-intercept**:
- The slope \( m \) is -3, which means for every 1 unit increase in \( x \), \( y \) decreases by 3 units.
- The y-intercept \( b \) is 2, which means the graph crosses the y-axis at the point (0, 2).
2. **Plot the y-intercept**:
- Start by plotting the point (0, 2) on the graph.
3. **Use the slope to find another point**:
- From the point (0, 2), apply the slope. Since the slope is -3, you can move down 3 units and 1 unit to the right:
1. From (0, 2), move down to 2 - 3 = -1, and move right to 1. This gives you the point (1, -1).
4. **Plot the second point**:
- Plot the point (1, -1) on the graph.
5. **Draw the line**:
- Draw a straight line through the points (0, 2) and (1, -1). Extend this line in both directions and add arrows at each end to indicate that it continues infinitely.
6. **Calculate additional points (optional)**:
- You could calculate more points by choosing different values for \( x \), substituting them into the equation \( y = -3x + 2 \), and plotting those points:
- For \( x = -1 \): \( y = -3(-1) + 2 = 5 \) → point (-1, 5)
- For \( x = 2 \): \( y = -3(2) + 2 = -4 \) → point (2, -4)
By following these steps, you will have a proper graph of the linear equation \( y = -3x + 2 \). The graph will slope downwards from left to right due to the negative slope.