Find an equation of the line in point-slope form that passes through the point (2, 1) and that is parallel to the given line. (Find the point-slope form by using 
(2, 1)
 as the primary point.)
y − 1 = −2(x − 7)
  
Incorrect: Your answer is incorrect.

To find the equation of a line in point-slope form that passes through the point \((2, 1)\) and is parallel to the given line, we'll follow these steps:

### Step 1: Identify the slope of the given line
The given line equation is:
\[
y - 1 = -2(x - 7)
\]
This is already in point-slope form:
\[
y - y_1 = m(x - x_1)
\]
where \(m\) is the slope. From the equation, we see that the slope \(m\) is \(-2\).

### Step 2: Use the slope for the new line
Since the new line is parallel to the given line, it will have the same slope. So, the slope of our new line is also \(-2\).

### Step 3: Write the equation in point-slope form
Using the point \((2, 1)\) and the slope \(-2\), we can write the equation in point-slope form:
\[
y - y_1 = m(x - x_1)
\]
Substituting the values:
\[
y - 1 = -2(x - 2)
\]

### Final Answer
The equation of the line in point-slope form is:
\[
\boxed{y - 1 = -2(x - 2)}
\]

This equation represents a line passing through the point \((2, 1)\) and is parallel to the given line.

Do you want further details, or have any questions about this?

Here are five related questions:
1. How do you convert the point-slope form to slope-intercept form?
2. What is the equation of the line perpendicular to the given line and passing through the point (2, 1)?
3. How do you determine if two lines are parallel given their equations?
4. What is the distance between the point (2, 1) and the line \(y - 1 = -2(x - 7)\)?
5. How do you find the equation of a line that passes through two given points?

**Tip:** Remember, parallel lines have the same slope but different y-intercepts unless they are identical lines.

Learn how to find the equation of a line in point-slope form that is parallel to a given line and passes through a specific point (2, 1). This example problem covers linear equations, point-slope form, and parallel lines conceptually. Suitable for high school students and beyond.

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