College Math Placement Practice Test

Which of the following represents the equation of a vertical line?

1. y = k

2. x = k

3. y = mx + b

4. None of the above

The correct answer is: x = k

The equation of a vertical line is represented by the form x = k, where k is a constant value. This indicates that for any value of y, the value of x remains constant at k. A vertical line runs up and down the Cartesian plane, so regardless of the height (y-coordinate), the position on the x-axis (x-coordinate) stays the same. In contrast, the other forms mentioned do not represent vertical lines. The equation y = k describes a horizontal line, where the y-coordinate remains constant while the x-coordinate can take on any value. The equation y = mx + b is the slope-intercept form of a linear equation, which defines lines that can have both a horizontal and vertical component depending on the slope (m) value. Therefore, it cannot represent a vertical line unless the slope is undefined, which is not indicated in the equation itself. Consequently, the only correct choice for representing a vertical line is x = k.