In the xy-plane, the graph of which of the following equations is a line with a slope of 3 ?

Options

A. `y=1/3x`
B. y = x − 3
C. y = 3x + 2
D. y = 6x + 3

Explanation

To determine which equation has a slope of 3, we can use the slope-intercept form of a linear equation, which is given by:

\[ y = mx + c \]

where:
- \( m \) is the slope of the line,
- \( c \) is the y-intercept.

We need to find the equation where \( m = 3 \).

### Step 1: Analyze the given options

Let's consider the options one by one and identify the slope from each equation.

### Step 2: Check each option

1. **Option A**: \( y = \frac{1}{3}x + 2 \)
- Here, the slope \( m = \frac{1}{3} \).
- **Conclusion**: This option does not have a slope of 3.

2. **Option B**: \( y = x - 3 \)
- Here, the slope \( m = 1 \).
- **Conclusion**: This option does not have a slope of 3.

3. **Option C**: \( y = 3x + 2 \)
- Here, the slope \( m = 3 \).
- **Conclusion**: This option has a slope of 3.

4. **Option D**: \( y = 6x + 3 \)
- Here, the slope \( m = 6 \).
- **Conclusion**: This option does not have a slope of 3.

### Step 3: Identify the correct option

From the analysis above, the only equation that has a slope of 3 is:

\[ \text{Option C: } y = 3x + 2 \]

### Final Answer:
The equation with a slope of 3 is \( y = 3x + 2 \).

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