Question

which equation represents a line which is parallel to $x = 0$?

answer
$y = 6$ $x = \frac{1}{3}y$
$y = x$ $x = 1$

Explanation:

Step1: Analyze the line \( x = 0 \)

The equation \( x = 0 \) represents the y - axis, which is a vertical line. Vertical lines have an undefined slope and are of the form \( x = k \), where \( k \) is a constant.

Step2: Analyze each option

• Option 1: \( y = 6 \) is a horizontal line (parallel to the x - axis) with a slope of 0. It is not parallel to \( x = 0 \).
• Option 2: \( x=\frac{1}{3}y \) can be rewritten as \( y = 3x \), which is a linear equation with a slope of 3. It is a non - vertical, non - horizontal line, so it is not parallel to \( x = 0 \).
• Option 3: \( y=x \) is a linear equation with a slope of 1. It is a non - vertical, non - horizontal line, so it is not parallel to \( x = 0 \).
• Option 4: \( x = 1 \) is a vertical line (since it is of the form \( x=k \) where \( k = 1\)). Vertical lines are parallel to each other, so \( x = 1 \) is parallel to \( x = 0 \).

Answer:

D. \( x = 1 \) (assuming the options are labeled as A. \( y = 6 \), B. \( x=\frac{1}{3}y \), C. \( y = x \), D. \( x = 1 \))