What is the equation of the line in slope-intercept form that passes through point (3, −2) and is parallel to the line y = 2x + 4? Show all necessary steps.

To find the equation of a line in slope-intercept form that passes through a specific point and is parallel to a given line, we can follow these steps:

### Step 1: Identify the slope of the given line.
The slope-intercept form of a line is given by:
\[
y = mx + b
\]
where \( m \) is the slope and \( b \) is the y-intercept.

For the given line \( y = 2x + 4 \), the slope \( m \) is 2.

### Step 2: Determine the slope of the parallel line.
Lines that are parallel have the same slope. Therefore, the slope of the line we are looking for is also \( m = 2 \).

### Step 3: Use the point-slope form to find the equation of the line.
The point-slope form of a line is:
\[
y - y_1 = m(x - x_1)
\]
where \( (x_1, y_1) \) is a point on the line.

We are given the point \( (3, -2) \) and the slope \( m = 2 \). Substituting these values into the point-slope form:
\[
y - (-2) = 2(x - 3)
\]
This simplifies to:
\[
y + 2 = 2(x - 3)
\]

### Step 4: Simplify to slope-intercept form.
Distribute the slope on the right side:
\[
y + 2 = 2x - 6
\]
Finally, subtract 2 from both sides to solve for \( y \):
\[
y = 2x - 8
\]

### Conclusion
The equation of the line in slope-intercept form that passes through the point \( (3, -2) \) and is parallel to the line \( y = 2x + 4 \) is:
\[
\boxed{y = 2x - 8}
\]

Would you like to know more details or have any questions?

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Here are five related questions for further practice:
1. What is the equation of the line that passes through point (5, 1) and is parallel to the line \( y = -3x + 7 \)?
2. How do you find the equation of a line perpendicular to \( y = 2x + 4 \) that passes through (3, -2)?
3. What is the slope of a line that is parallel to the line \( y = \frac{1}{2}x - 3 \)?
4. How do you determine if two lines are parallel given their equations?
5. What is the equation of a line with slope 4 passing through the point (-1, 3)?

**Tip:** When determining if two lines are parallel, always compare their slopes. If the slopes are equal, the lines are parallel.

Learn how to find the equation of a line in slope-intercept form that is parallel to y = 2x + 4 and passes through point (3, -2). Detailed step-by-step solution provided.

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