Question

question
which equation represents a line which is perpendicular to the y - axis?
answer
$y = x + 3$
$y = 2$
$x = - 4$
$y = x$

Explanation:

Step1: Recall the properties of lines perpendicular to the y - axis

A line perpendicular to the y - axis is a horizontal line. The equation of a horizontal line is of the form \(y = k\), where \(k\) is a constant.

Step2: Analyze each option

• For \(y=x + 3\), this is a line with slope \(m = 1\) (in the form \(y=mx + b\)), so it is not horizontal.
• For \(y=x\), this is a line with slope \(m = 1\) (in the form \(y=mx\)), so it is not horizontal.
• For \(x=-4\), this is a vertical line (perpendicular to the x - axis).
• For \(y = 2\), this is in the form \(y=k\) (\(k = 2\)), which represents a horizontal line. A horizontal line is perpendicular to the vertical y - axis.

Answer:

\(y = 2\)