Question

find the equation and slope of a line that is parallel to the y-axis and passes through the point (3, 1). click on \undefined\ as the answer if necessary.
equation:
slope:

Explanation:

Step1: Recall vertical line properties

A line parallel to the \( y \)-axis is a vertical line. The equation of a vertical line passing through a point \( (a, b) \) is \( x = a \). Here, the point is \( (3, 1) \), so the equation is \( x = 3 \).

Step2: Determine the slope of vertical line

The slope of a line is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). 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: \( x = 3 \)
Slope: Undefined