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Let's solve the problem in detail.

We need to write the equation of a line that is **parallel** to \( y = 3x - 2 \) and passes through the point \( (3, 2) \).

### Step 1: Determine the slope
Since the line is parallel to \( y = 3x - 2 \), it has the **same slope**. The slope-intercept form of a line is:

\[
y = mx + b
\]

where \( m \) is the slope. From the given equation \( y = 3x - 2 \), the slope is \( m = 3 \).

### Step 2: Use Point-Slope Form
The point-slope form of a line is:

\[
y - y_1 = m(x - x_1)
\]

Here, \( (x_1, y_1) = (3, 2) \) is the point the line passes through, and the slope \( m = 3 \). Plugging in these values:

\[
y - 2 = 3(x - 3)
\]

This is the **point-slope form** of the equation.

### Step 3: Convert to Slope-Intercept Form
Now, let's simplify the point-slope form into slope-intercept form \( y = mx + b \).

\[
y - 2 = 3(x - 3)
\]
\[
y - 2 = 3x - 9
\]
\[
y = 3x - 9 + 2
\]
\[
y = 3x - 7
\]

This is the equation of the line in **slope-intercept form**.

### Final Answer:
1. **Point-Slope Form:** \( y - 2 = 3(x - 3) \)
2. **Slope-Intercept Form:** \( y = 3x - 7 \)

Would you like any additional details or clarifications?

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Here are 5 related questions you might consider:
1. How do we find the slope of a line given two points?
2. What is the general process for converting from point-slope form to slope-intercept form?
3. How do we find the equation of a line that is perpendicular to another line?
4. What happens if two lines have the same slope but different intercepts?
5. How do we determine the distance between a point and a line?

**Tip:** Remember, parallel lines always have the same slope but different y-intercepts!

Write the equation of a line that is parallel to y = 3x - 2 and passes through the point (3, 2).

Learn how to write the equation of a line that is parallel to y = 3x - 2 and passes through the point (3, 2). This problem explores key concepts in linear equations, including point-slope form and slope-intercept form. Suitable for students in Grades 7-9.

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