What is the equation, in slope-intercept form, of the line that is perpendicular to the given line and passes through the point (2, −1)? 

To find the equation of a line that is **perpendicular** to a given line and passes through the point \((2, -1)\), follow these steps:

### 1. **Determine the slope of the given line:**
The **slope-intercept form** of a line is:

\[
y = mx + b
\]

where \(m\) is the slope and \(b\) is the y-intercept.

You haven't provided the equation of the given line, so let's proceed with the idea that it has some slope, \(m_1\).

### 2. **Find the slope of the perpendicular line:**
The slopes of two perpendicular lines are **negative reciprocals** of each other. If the slope of the given line is \(m_1\), the slope of the line perpendicular to it is:

\[
m_2 = -\frac{1}{m_1}
\]

### 3. **Use the point-slope form:**
Since the line you're looking for passes through the point \((2, -1)\), you can use the **point-slope form** of a line equation:

\[
y - y_1 = m_2 (x - x_1)
\]

Substitute \((x_1, y_1) = (2, -1)\) and the slope \(m_2\) you found:

\[
y + 1 = m_2(x - 2)
\]

### 4. **Convert to slope-intercept form:**
Now solve for \(y\) to convert this equation into slope-intercept form \(y = mx + b\).

If you provide the equation of the given line, I can calculate the exact slope of the perpendicular line and give you the final equation.

Would you like more details on a specific part of this? 
Here are 5 related questions to explore further:

1. What is the general formula for negative reciprocals?
2. How do you find the slope of a line from its equation?
3. What is the geometric significance of perpendicular slopes?
4. How would you write the equation if the point were different?
5. How can you check if two lines are perpendicular?

**Tip:** To quickly find the negative reciprocal of a number, flip the fraction and change the sign!

What is the equation, in slope-intercept form, of the line that is perpendicular to the given line and passes through the point (2, −1)?

Learn how to derive the equation of a line that is perpendicular to a given line and passes through the point (2, −1). This solution covers slope-intercept form, point-slope form, and the concept of negative reciprocals for perpendicular lines. Ideal for students in Grades 8-10.

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