Question

find the equation and slope of a line that is perpendicular to the y-axis and passes through the point (-2, 3). necessary.
equation:
slope:

Explanation:

Step1: Analyze the line's orientation

A line perpendicular to the \( y \)-axis is horizontal. Horizontal lines have the equation form \( y = k \), where \( k \) is a constant (the \( y \)-coordinate of all points on the line).

Step2: Determine the equation using the point

The line passes through \( (-2, 3) \). For a horizontal line, the \( y \)-coordinate is constant. So the equation is \( y = 3 \).

Step3: Find the slope of a horizontal line

The slope of a horizontal line is \( 0 \) (since the change in \( y \) (\( \Delta y \)) is \( 0 \), and slope \( m=\frac{\Delta y}{\Delta x} \), so \( m = 0 \) when \( \Delta y = 0 \)).

Answer:

Equation: \( y = 3 \)
Slope: \( 0 \)