Question
Create a graph showing a line passing through the point of 0, 3 with the slope of -2/3
Answers
GPT-4o mini
While I can't create visual images directly, I can guide you on how to graph the line with a slope of -2/3 that passes through the point (0, 3).
### Steps to Create the Graph:
1. **Identify the Point**: Start by marking the point (0, 3) on a coordinate plane. This point is on the y-axis.
2. **Use the Slope**: The slope of the line is -2/3. This means that for every 3 units you move to the right (positive x-direction), you move down 2 units (because the slope is negative).
3. **Find Another Point**:
- From (0, 3), move 3 units to the right (to x = 3).
- From that point, move down 2 units to (3, 1).
4. **Plot the Second Point**: Mark the point (3, 1) on your graph.
5. **Draw the Line**: Connect the points (0, 3) and (3, 1) with a straight line, extending in both directions.
6. **Optional - Find More Points**:
- If you want additional points, you can continue using the slope. From (3, 1), move another 3 units right and down 2: (6, -1). You can also do it in the opposite direction from (0, 3) going left to (-3, 5).
### Equation of the Line:
If you want the equation of the line, you can use the point-slope form:
\[ y - y_1 = m(x - x_1) \]
where \( m \) is the slope and \( (x_1, y_1) \) is the point (0, 3).
Substituting in the values:
\[ y - 3 = -\frac{2}{3}(x - 0) \]
Simplifying gives:
\[ y = -\frac{2}{3}x + 3 \]
You can use this equation to plot additional points if needed.
### Summary:
- Start at (0, 3)
- Move 3 units right and 2 units down to find (3, 1)
- Draw the line through these two points.
### Steps to Create the Graph:
1. **Identify the Point**: Start by marking the point (0, 3) on a coordinate plane. This point is on the y-axis.
2. **Use the Slope**: The slope of the line is -2/3. This means that for every 3 units you move to the right (positive x-direction), you move down 2 units (because the slope is negative).
3. **Find Another Point**:
- From (0, 3), move 3 units to the right (to x = 3).
- From that point, move down 2 units to (3, 1).
4. **Plot the Second Point**: Mark the point (3, 1) on your graph.
5. **Draw the Line**: Connect the points (0, 3) and (3, 1) with a straight line, extending in both directions.
6. **Optional - Find More Points**:
- If you want additional points, you can continue using the slope. From (3, 1), move another 3 units right and down 2: (6, -1). You can also do it in the opposite direction from (0, 3) going left to (-3, 5).
### Equation of the Line:
If you want the equation of the line, you can use the point-slope form:
\[ y - y_1 = m(x - x_1) \]
where \( m \) is the slope and \( (x_1, y_1) \) is the point (0, 3).
Substituting in the values:
\[ y - 3 = -\frac{2}{3}(x - 0) \]
Simplifying gives:
\[ y = -\frac{2}{3}x + 3 \]
You can use this equation to plot additional points if needed.
### Summary:
- Start at (0, 3)
- Move 3 units right and 2 units down to find (3, 1)
- Draw the line through these two points.