Question

which statements are true? check all that apply. the line x = 0 is perpendicular to the line y = –3. all lines that are parallel to the y-axis are vertical lines. all lines that are perpendicular to the x-axis have a slope of 0. the equation of the line parallel to the x-axis that passes through the point (2, –6) is x = 2. the equation of the line perpendicular to the y-axis that passes through the point (–5, 1) is y = 1.

Answer 1

1) True that line x = 0 is perpedicular to y = -3. Because x = 0 is parallel to the y-axis and y = -3 is parallel to the x-axis.

2) True that all the lines that are parallel to the y-axis are vertucal lines (the y-axis is vertical)

3) False that all lines perpendicular to the x-axis have a slope o 0. Their slope trends to infinity.

4) False that the equation of the line parallel to the x-axis that passes through the point (2, –6) is x = 2. The right equation is y = - 6

5) True thath the equation of the line perpendicular to the y-axis that passes through the point (–5, 1) is y = 1

Answer 2

The correct answers are:

The line x = 0 is perpendicular to the line y = –3; all lines that are parallel to the y-axis are vertical lines; the equation of the line perpendicular to the y-axis that passes through the point (–5, 1) is y = 1.

Explanation:

The line x=0 is the x-axis. The line y=-3 is a vertical line. These two will be perpendicular by definition; x=0 has a slope of 0 while y=-3 has an undefined slope. Additionally, a horizontal line will always be perpendicular to a vertical line.

In order for a line to be parallel to the y-axis, it must have the same slope as the y-axis; this means it must be a vertical line.

In order for a line to be perpendicular to the y=axis, it must be a horizontal line. The line y=1 is a horizontal line that passes through 1 on the y-axis.