Question

which equation represents a line which is perpendicular to $x = 0$?
answer
$x=-y$
$x = -5$
$y=x + 2$
$y = 1$

Explanation:

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

The line \(x=0\) is a vertical line (the \(y -\)axis). A line perpendicular to a vertical line is a horizontal line.

Step2: Recall the form of a horizontal line

The equation of a horizontal line is of the form \(y = k\), where \(k\) is a constant.

Step3: Check each option

• For \(x=-y\), it can be rewritten as \(y=-x\), which is a non - vertical and non - horizontal line (a line with slope \(- 1\)).
• For \(x = - 5\), it is a vertical line (parallel to \(x = 0\)).
• For \(y=x + 2\), it is a line with slope \(1\) (non - vertical and non - horizontal).
• For \(y = 1\), it is a horizontal line (of the form \(y=k\) where \(k = 1\)).

Answer:

\(y = 1\)