Question

find the equation and slope of a line that is parallel to the y-axis and passes through the point (8, 1). click on \undefined\ as the answer if necessary.
equation:
slope:

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.

Step2: Determine the equation

The line passes through the point \( (8, 1) \), so the \( x \)-coordinate is \( 8 \). Thus, the equation of the line is \( x = 8 \).

Step3: Determine the slope

The slope of a vertical line is undefined because the slope formula \( m=\frac{y_2 - y_1}{x_2 - x_1} \) results in a division by zero (since \( x_2 - x_1 = 0 \) for a vertical line).

Answer:

Equation: \( x = 8 \)
Slope: Undefined