Question
What is the equation of the line that passes through the point \( (6,-3) \) and has an undefined slope?
Ask by Harris Montgomery. in the United States
Jan 01,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The equation of the vertical line passing through the point \( (6, -3) \) is \( x = 6 \).
Solution
A line with an **undefined slope** is a **vertical line**. Vertical lines have the same \( x \)-coordinate for every point on the line.
Given the point \( (6, -3) \), the vertical line passing through this point will have the equation:
\[
x = 6
\]
**Explanation:**
- **Undefined Slope:** Vertical lines do not have a defined slope because the change in \( x \) is zero, and division by zero is undefined.
- **Equation of a Vertical Line:** All points on a vertical line share the same \( x \)-coordinate. Therefore, if the line passes through \( x = 6 \), its equation is simply \( x = 6 \).
So, the equation of the line that passes through \( (6, -3) \) with an undefined slope is:
\[
\boxed{x = 6}
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
When a line has an undefined slope, it means that the line is vertical. For vertical lines, the equation is of the form \( x = a \), where \( a \) is the x-coordinate of any point on the line. Since the line in question passes through the point \( (6, -3) \), the equation of the line is simply \( x = 6 \). Moreover, think of how vertical lines work: they rise straight up and down, infinitely in both directions, making them a great representation of unique x-values. So no matter what y-value you plug in, you’ll always find yourself right above or below that x-coordinate!
