Question

question which equation represents a line which is parallel to y = 0? answer ○ x = 1 ○ y = x + 3 ○ y = x ○ y = 6

Explanation:

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

The equation \( y = 0 \) represents the x - axis. The x - axis is a horizontal line, and the slope of a horizontal line is \( 0 \). A line parallel to a horizontal line must also be horizontal. The equation of a horizontal line is of the form \( y = k \), where \( k \) is a constant.

Step2: Analyze each option

• Option \( x = 1 \): This is a vertical line (parallel to the y - axis), and its slope is undefined. So it is not parallel to \( y = 0 \).
• Option \( y=x + 3 \): The slope of this line is \( 1 \) (from the slope - intercept form \( y=mx + b \), where \( m \) is the slope). A line with slope \( 1 \) is not parallel to a horizontal line (slope \( 0 \)).
• Option \( y=x \): The slope of this line is \( 1 \), so it is not parallel to \( y = 0 \).
• Option \( y = 6 \): This is a horizontal line (since it is of the form \( y=k \) with \( k = 6 \)) and has a slope of \( 0 \), which is the same as the slope of \( y = 0 \). So \( y = 6 \) is parallel to \( y = 0 \).

Answer:

\( y = 6 \) (the option: \( y = 6 \))