Question

20.
Graph the function.

For the function whose graph is shown below, which is the correct formula for the function?







y = –3x – 1


y = 3x + 1


y = –3x + 1


y = 3x – 1

Answer 1

To determine the correct formula for the function based on the options you've provided, we'll need to analyze the slope and y-intercept of the graph of each equation.

### General Form of Linear Equation
The general form of a linear equation is \(y = mx + b\) where:
- \(m\) is the slope of the line.
- \(b\) is the y-intercept (the value of \(y\) when \(x = 0\)).

### Analyzing Each Option
1. **y = –3x – 1**
- Slope (m): -3
- Y-Intercept (b): -1

2. **y = 3x + 1**
- Slope (m): 3
- Y-Intercept (b): +1

3. **y = –3x + 1**
- Slope (m): -3
- Y-Intercept (b): +1

4. **y = 3x – 1**
- Slope (m): 3
- Y-Intercept (b): -1

### Steps to Identify the Correct Equation
1. **Identify the slope:** Check if the line is increasing or decreasing. If it goes up from left to right, the slope is positive (options with +3). If it goes down, the slope is negative (options with -3).

2. **Identify the y-intercept:** Look at where the line crosses the y-axis.

### Conclusion
Without the graphical representation, I'm unable to define the characteristics of the line directly. However, if you can provide the slope (increasing or decreasing) and the y-intercept from the graph, I can assist in confirming which equation matches the function displayed.

- If the slope is negative and the line crosses the y-axis at -1, choose \(y = –3x – 1\).
- If the slope is negative and it crosses at +1, choose \(y = –3x + 1\).
- If the slope is positive and it crosses at +1, choose \(y = 3x + 1\).
- If the slope is positive and it crosses at -1, choose \(y = 3x - 1\).

Please provide further information from the graph if available!