Question

1 which of the following is not true about vertical lines? a vertical lines are perpendicular to the x - axis. b vertical lines are parallel to the y - axis. c vertical lines have undefined slope. d vertical lines have equations of the form ( y = b ).

Explanation:

• Option A: Vertical lines are perpendicular to the \(x -\)axis. Since the \(x -\)axis is horizontal, vertical lines form a \(90^{\circ}\) angle with it, so this is true.
• Option B: The \(y -\)axis is vertical. Vertical lines are parallel to each other, so vertical lines are parallel to the \(y -\)axis. This is true.
• Option C: The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). For a vertical line \(x_2=x_1\), so \(m=\frac{y_2 - y_1}{0}\), which is undefined. This is true.
• Option D: The equation of a vertical line is of the form \(x = a\) (where \(a\) is a constant). The equation \(y=b\) represents a horizontal line (parallel to the \(x -\)axis). This is false.

Answer:

D. Vertical lines have equations of the form \(y = b\).