Question

which equation represents a line which is parallel to the y-axis?

answer

\\( x = 2 \\)
\\( y = 1 \\)
\\( x = \frac{1}{5}y \\)
\\( x = 3y \\)

Explanation:

Step1: Recall vertical line properties

A line parallel to the \( y \)-axis is a vertical line. The equation of a vertical line is of the form \( x = a \), where \( a \) is a constant (this means \( x \) has a fixed value, and \( y \) can be any real number).

Step2: Analyze each option

• Option \( x = 2 \): This is in the form \( x = a \) (where \( a = 2 \)), so it represents a vertical line (parallel to the \( y \)-axis).
• Option \( x=\frac{1}{5}y \): This can be rewritten as \( y = 5x \), which is a linear equation with a slope (a non - vertical, non - horizontal line with slope 5).
• Option \( y = 1 \): This is a horizontal line (parallel to the \( x \)-axis), since \( y \) has a fixed value and \( x \) can be any real number.
• Option \( x = 3y \): This can be rewritten as \( y=\frac{1}{3}x \), which is a linear equation with a slope (a non - vertical, non - horizontal line with slope \( \frac{1}{3} \)).

Answer:

A. \( x = 2 \)