Question
What is the shape of the graph y = 3x + 2
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GPT-4o mini
The equation \( y = 3x + 2 \) represents a linear function. The graph of this equation is a straight line.
Here are some key characteristics of the graph:
1. **Slope**: The coefficient of \( x \) is 3, which means the slope of the line is 3. This indicates that for every unit increase in \( x \), \( y \) increases by 3 units.
2. **Y-intercept**: The constant term is 2, so the line intersects the y-axis at the point (0, 2).
3. **Direction**: Since the slope is positive, the line rises as it moves from left to right.
To visualize it, you can plot a few points. For example:
- When \( x = 0 \), \( y = 2 \) (point (0, 2))
- When \( x = 1 \), \( y = 3(1) + 2 = 5 \) (point (1, 5))
- When \( x = -1 \), \( y = 3(-1) + 2 = -1 \) (point (-1, -1))
Plotting these points and drawing a line through them will give you the graph of \( y = 3x + 2 \).
Here are some key characteristics of the graph:
1. **Slope**: The coefficient of \( x \) is 3, which means the slope of the line is 3. This indicates that for every unit increase in \( x \), \( y \) increases by 3 units.
2. **Y-intercept**: The constant term is 2, so the line intersects the y-axis at the point (0, 2).
3. **Direction**: Since the slope is positive, the line rises as it moves from left to right.
To visualize it, you can plot a few points. For example:
- When \( x = 0 \), \( y = 2 \) (point (0, 2))
- When \( x = 1 \), \( y = 3(1) + 2 = 5 \) (point (1, 5))
- When \( x = -1 \), \( y = 3(-1) + 2 = -1 \) (point (-1, -1))
Plotting these points and drawing a line through them will give you the graph of \( y = 3x + 2 \).
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