Question

select the correct answer. which of the equations below represents a line perpendicular to the x-axis? a. x = 3 b. x = 3y c. x = y d. x = -3y

Explanation:

Step1: Recall x - axis properties

The x - axis is horizontal, so a line perpendicular to it is vertical.

Step2: Analyze vertical line equation

A vertical line has the equation \( x = a \) (where \( a \) is a constant), as it has an undefined slope and all points on it have the same x - coordinate.

Step3: Evaluate each option

• Option A: \( x = 3 \) is a vertical line (constant x - value), so it is perpendicular to the x - axis.
• Option B: \( x = 3y \) can be rewritten as \( y=\frac{1}{3}x \), which is a non - vertical, non - horizontal line with slope \( \frac{1}{3} \).
• Option C: \( x = y \) can be rewritten as \( y = x \), which is a line with slope 1, not perpendicular to the x - axis.
• Option D: \( x=-3y \) can be rewritten as \( y =-\frac{1}{3}x \), which is a line with slope \( -\frac{1}{3} \), not perpendicular to the x - axis.

Answer:

A. \( x = 3 \)