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.

Explanation:

Step1: Analyze the first statement

The line $x = 0$ is the $y$-axis and $y=-3$ is a horizontal line. Perpendicular lines have slopes that are negative - reciprocals. The slope of $x = 0$ is undefined and the slope of $y=-3$ is $0$, so they are perpendicular.

Step2: Analyze the second statement

Lines parallel to the $y$-axis have the form $x = k$ (where $k$ is a constant), and these are vertical lines.

Step3: Analyze the third statement

Lines perpendicular to the $x$-axis are vertical lines. The slope of a vertical line is undefined, not $0$.

Step4: Analyze the fourth statement

A line parallel to the $x$-axis has the form $y = k$. The line passing through $(2,-6)$ and parallel to the $x$-axis is $y=-6$, not $x = 2$.

Step5: Analyze the fifth statement

A line perpendicular to the $y$-axis is a horizontal line. The equation of a horizontal line passing through the point $(-5,1)$ is $y = 1$.

Answer:

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 $y = 1$.