Question

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

Explanation:

Step1: Recall properties of vertical lines

A line parallel to the \( y \)-axis is a vertical line. The equation of a vertical line is of the form \( x = a \), where \( a \) is the \( x \)-coordinate of any point on the line.
Since the line passes through \( (4, -6) \), the \( x \)-coordinate is 4, so the equation is \( x = 4 \).

Step2: Determine the slope of a vertical line

The slope of a line is calculated as \( m=\frac{y_2 - y_1}{x_2 - x_1} \). For a vertical line, the \( x \)-coordinates of all points are the same, so \( x_2 - x_1 = 0 \). Division by zero is undefined, so the slope of a vertical line is undefined.

Answer:

Equation: \( x = 4 \)
Slope: Undefined