Question
A line passes through \( (-9,-6) \) and has an undefined slope. Write an equation of line satisfying the given conditions.
Ask by Carrillo Hodgson. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The equation of the line is \( x = -9 \).
Solution
A line with an **undefined slope** is a **vertical line**. Vertical lines run parallel to the y-axis and have the same x-coordinate for every point on the line.
Given the line passes through the point \((-9, -6)\), the x-coordinate of all points on this line will be \(-9\).
**Equation of the Line:**
\[
x = -9
\]
**Explanation:**
1. **Understanding Slope:**
- The **slope** of a line measures its steepness.
- A **vertical line** has an undefined slope because the change in x (Δx) is zero, and division by zero is undefined.
2. **Equation of a Vertical Line:**
- The general form of a vertical line is \(x = k\), where \(k\) is the constant x-value for all points on the line.
3. **Applying the Given Point:**
- Since the line passes through \((-9, -6)\), the x-value for all points on the line must be \(-9\).
Therefore, the equation of the line is:
\[
\boxed{x = -9}
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
When a line has an undefined slope, it means it's a vertical line. Vertical lines can be represented by equations in the form \( x = k \), where \( k \) is the x-coordinate of any point lying on the line. Since our line passes through the point \( (-9, -6) \), the equation of the line is simply \( x = -9 \). So, there you have it! This line runs straight up and down at \( x = -9 \), making it perfectly vertical.
