Question
Describe the graph of \( y=3 x-1 \) * Increasing Decreasing Constant
Ask by Fitzgerald Lee. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The graph of \( y = 3x - 1 \) is a straight line that is increasing.
Solution
The graph of the equation \( y = 3x - 1 \) is a **straight line**. To determine its behavior, we can analyze the slope and the y-intercept:
1. **Slope (\( m \))**: The coefficient of \( x \) is **3**, which is positive. A positive slope means that as \( x \) increases, \( y \) also increases. Therefore, the line is **increasing**.
2. **Y-intercept (\( b \))**: The constant term is **-1**, which means the line crosses the y-axis at the point \( (0, -1) \).
### Summary:
- **Graph Type**: Straight line
- **Slope**: Positive (\( m = 3 \))
- **Behavior**: **Increasing**
**Answer:**
The graph of \( y = 3x - 1 \) is a straight line that is increasing.
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Simplify this solution Beyond the Answer
The graph of \( y = 3x - 1 \) is increasing because as the value of \( x \) increases, the value of \( y \) also increases. The slope of the line is positive (3), which means for every unit increase in \( x \), \( y \) increases by 3 units. This creates a straight line that rises as it moves from left to right. Additionally, this linear function intersects the y-axis at -1, which is its y-intercept. This means that when \( x = 0 \), the value of \( y \) is -1. The graph will continue to rise above this point moving upward as \( x \) increases, showcasing its increasing nature clearly!
