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 first statement

$x=0$ is the vertical y-axis; $y=-3$ is a horizontal line. Vertical and horizontal lines are perpendicular. This statement is true.

Step2: Analyze second statement

Lines parallel to the y-axis run straight up/down, which are vertical lines. This statement is true.

Step3: Analyze third statement

Lines perpendicular to the x-axis are vertical, which have an undefined slope (not 0; slope 0 is horizontal lines parallel to x-axis). This statement is false.

Step4: Analyze fourth statement

Lines parallel to the x-axis are horizontal, with equations of the form $y=k$. For point $(2,-6)$, the equation is $y=-6$, not $x=2$. This statement is false.

Step5: Analyze fifth statement

Lines perpendicular to the y-axis are horizontal, with equations $y=k$. For point $(-5,1)$, $k=1$, so equation is $y=1$. This statement is true.

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 $y = 1$.