Question

which equation represents a line which is parallel to ( x = 0 )?
answer
( circ x = 8 )
( circ x = \frac{1}{4}y )
( circ y = 5 )
( circ x = -3y )

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 their equations are of the form \( x = k \), where \( k \) is a constant.

Step2: Analyze each option

• Option 1: \( x = 8 \) is a vertical line (since it is of the form \( x=k \) with \( k = 8 \)). Vertical lines are parallel to each other because they have the same undefined slope.
• Option 2: \( x=\frac{1}{4}y \) can be rewritten as \( y = 4x \), which is a linear equation with a slope of 4. It is a non - vertical line, so it is not parallel to \( x = 0 \).
• Option 3: \( y = 5 \) is a horizontal line (it has a slope of 0). Horizontal lines are perpendicular to vertical lines, so it is not parallel to \( x = 0 \).
• Option 4: \( x=-3y \) can be rewritten as \( y=-\frac{1}{3}x \), which is a linear equation with a slope of \( -\frac{1}{3} \). It is a non - vertical line, so it is not parallel to \( x = 0 \).

Answer:

\( x = 8 \) (the option with \( x = 8 \))