Question

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

Explanation:

Step1: Identify line orientation

A line perpendicular to the y-axis is horizontal.

Step2: Write horizontal line equation

Horizontal lines have the form $y = k$, where $k$ is the y-coordinate of the point the line passes through. For point $(-4, 6)$, $k=6$, so $y=6$.

Step3: Calculate slope of horizontal line

The slope of a horizontal line is 0, as there is no vertical change over any horizontal change: $\text{slope} = \frac{\Delta y}{\Delta x} = \frac{0}{\Delta x} = 0$.

Answer:

Equation: $y=6$
Slope: $0$