Question

find the equation and slope of a line that is perpendicular to the line x = -6 and passes through the point (-4, -6). click on \undefined\ as the answer if necessary.
equation:
slope:

Explanation:

Step1: Analyze the given line

The line \( x = -6 \) is a vertical line (since it has the form \( x = \text{constant} \)). Vertical lines have an undefined slope.

Step2: Determine the perpendicular line

A line perpendicular to a vertical line is a horizontal line. Horizontal lines have the equation of the form \( y = \text{constant} \) and a slope of \( 0 \).

Step3: Find the equation of the horizontal line

The horizontal line passes through the point \( (-4, -6) \). For a horizontal line, the \( y \)-coordinate is constant. So the equation is \( y = -6 \).

Step4: Confirm the slope

As horizontal lines have a slope of \( 0 \), the slope of \( y = -6 \) is \( 0 \).

Answer:

Equation: \( y = -6 \)
Slope: \( 0 \)