Find the equation of a line perpendicular to x + y = -10 that passes
through the point (-5, - 7).

To find the equation of the line that is perpendicular to \( x + y = -10 \) and passes through the point \( (-5, -7) \), we can follow these steps:

### Step 1: Find the slope of the given line
The given equation is:
\[
x + y = -10
\]
This can be rewritten in slope-intercept form ( \( y = mx + b \) ):
\[
y = -x - 10
\]
The slope \( m_1 \) of this line is \( -1 \).

### Step 2: Find the slope of the perpendicular line
The slope of the line perpendicular to another line is the negative reciprocal of the original slope. Since the slope of the given line is \( -1 \), the slope \( m_2 \) of the perpendicular line is:
\[
m_2 = \frac{1}{-(-1)} = 1
\]

### Step 3: Use the point-slope form to find the equation
The point-slope form of a line is:
\[
y - y_1 = m(x - x_1)
\]
where \( (x_1, y_1) \) is the point the line passes through and \( m \) is the slope. We know the slope is 1, and the point is \( (-5, -7) \). Substituting these values:
\[
y - (-7) = 1(x - (-5))
\]
Simplifying this:
\[
y + 7 = 1(x + 5)
\]
\[
y + 7 = x + 5
\]
\[
y = x - 2
\]

### Final Answer:
The equation of the line perpendicular to \( x + y = -10 \) that passes through the point \( (-5, -7) \) is:
\[
y = x - 2
\]

Would you like more details or have any questions?

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Here are 5 related questions:
1. How do you find the equation of a line given two points?
2. What is the relationship between slopes of parallel lines?
3. How do you convert a line equation from standard form to slope-intercept form?
4. Can the slope of a line be undefined? What does that mean geometrically?
5. How do you find the equation of a line parallel to a given line?

**Tip:** The slope-intercept form, \( y = mx + b \), is useful for quickly identifying the slope and y-intercept of a line.

Find the equation of a line perpendicular to x + y = -10 that passes through the point (-5, -7).

Learn how to find the equation of a line that is perpendicular to x + y = -10 and passes through the point (-5, -7). This solution uses algebraic concepts such as slopes, perpendicular lines, and the point-slope form to derive the final equation. Suitable for students in Grades 8-10.

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