UGA Math Placement Practice Exam

The equation that represents a vertical line is given by "x = 4." A vertical line in a Cartesian coordinate system is characterized by having the same x-coordinate for all points on that line, which means that the y-coordinate can be any value. In this case, "x = 4" indicates that no matter the value of y, the x-coordinate will always remain 4. This results in a straight line that runs vertically through the point (4, y), where y can be any real number.

In contrast, the equation "y = 2" describes a horizontal line where the y-coordinate remains constant at 2, regardless of the x-coordinate. The equation "y = mx + b" represents a linear function with a slope (m) that can vary, resulting in a line that is not vertical unless m is infinite, which is not a valid representation. Lastly, "y = x" denotes a diagonal line with a slope of 1, indicating that as x increases, y also increases at the same rate, rather than being a vertical line.