Which equation represents a line which is perpendicular to the $y$-axis?

A. $y=-6$
B. $x=-6$
C. $x=\frac{1}{2} y$
D. $x=-y$

A line perpendicular to the y -axis is a horizontal line.
A horizontal line has the equation y = c , where c is a constant.
Among the given options, only y = − 6 fits this form.
Therefore, the equation representing a line perpendicular to the y -axis is y = − 6 ​ .

Explanation

Problem Analysis The problem asks us to identify the equation of a line that is perpendicular to the y -axis. In other words, we are looking for a horizontal line.

Analyze the options A line perpendicular to the y -axis is a horizontal line. Horizontal lines have the form y = c , where c is a constant. Let's examine the given options:



y = − 6 : This is in the form y = c , where c = − 6 . This represents a horizontal line.
x = − 6 : This represents a vertical line.
x = 2 1 ​ y : This can be rewritten as y = 2 x , which is a line passing through the origin with a slope of 2.
x = − y : This can be rewritten as y = − x , which is a line passing through the origin with a slope of -1.


Identify the correct equation The equation y = − 6 is the only equation that represents a horizontal line, which is perpendicular to the y -axis.

Final Answer Therefore, the equation that represents a line perpendicular to the y -axis is y = − 6 .


Examples
Understanding lines perpendicular to the y-axis is crucial in various real-world applications. For example, when designing a building, architects need to ensure that floors are perfectly horizontal, which means they are perpendicular to the vertical axis (y-axis). Similarly, in mapping and navigation, latitude lines are perpendicular to the longitude lines, which can be thought of as the y-axis on a map. This concept ensures accurate positioning and direction.

Answered by GinnyAnswer | 2025-07-08