Question

Which statements are true Select three options.

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

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 parallel to the x-axis that passes through the point (2,6) is x = 2.

Step-by-step explanation:

Mathematical lines are one-dimensional geometric objects defined by an infinite set of points extending in opposite directions. Described by linear equations, lines can take various forms such as horizontal, vertical, or slanted. Slope-intercept form (y = mx + b) is commonly used to represent lines, specifying their slope and y-intercept. The statements that are true are:

1. The line x = 0 is perpendicular to the line y = -3.
2. All lines that are parallel to the y-axis are vertical lines.
3. The equation of the line parallel to the x-axis that passes through the point (2,6) is x = 2.

Answer 2

The line x = 0 is perpendicular to the line y = -3:

Correct. Any horizontal line (y = a) and any vertical line (x = b) intersect at some point and are perpendicular.

All lines that are parallel to the y-axis are vertical lines:

Correct. The y-axis is a vertical line, so any lines that are parallel to it must also be vertical.

All lines that are perpendicular to the x-axis have a slope of 0.

Incorrect. Lines that have a slope of 0 are horizontal, and the x-axis is horizontal as well. Any lines with a slope of 0 are parallel to the x-axis, not perpendicular to it.

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

Incorrect. x = 2 is a vertical line, and vertical lines cannot be parallel to the horizontal x-axis. x = 2 is perpendicular to the x-axis, however.

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

Correct. The line y = 1 is horizontal, and the y-axis is a vertical line. Because the line y = 1 crosses the y-axis, the lines are perpendicular.