Question

select the correct answer. which of the equations below represents a line perpendicular to the y-axis? a. y = x b. y = -6 c. x = 6 d. y = 6x

Explanation:

Step1: Recall y - axis properties

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

Step2: Analyze equation types

• For option A: The equation \( y=x \) has a slope of \( 1 \), it is a diagonal line, not horizontal.
• For option B: The equation \( y = - 6 \) represents a horizontal line (since for all values of \( x \), \( y\) is always \( - 6 \)). A horizontal line is perpendicular to the vertical \( y \) - axis.
• For option C: The equation \( x = 6 \) represents a vertical line, which is parallel to the \( y \) - axis, not perpendicular.
• For option D: The equation \( y=6x \) has a slope of \( 6 \), it is a diagonal line, not horizontal.

Answer:

B. \( y = -6 \)