Final answer:
The equation x = -5 represents a vertical line, which is parallel to the y-axis and has no slope, as it does not depend on the y-coordinate values. This line crosses the x-axis at the point (-5, 0). Vertical lines have undefined slopes and do not conform to the standard slope-intercept form of a line. The correct option is B.
Step-by-step explanation:
The equation given is x = -5, which represents a vertical line. In the context of the Cartesian coordinate system, the equation x = a, where a is a constant, signifies that the x-coordinate of every point on the line is equal to a, and it does not depend on the value of the y-coordinate. Consequently, this line is parallel to the y-axis and is a vertical line with no slope, as the value of x never changes regardless of the value of y.
Contrary to a vertical line, a horizontal line in the plane has the form y = b, where b is also a constant. This indicates that the y-coordinate stays constant while the x-coordinate can take any value. Referring back to the initial equation, x = -5, we can confirm that it signifies a vertical line that crosses the x-axis at -5.
To visualize this, consider the properties of the slope (m) and y-intercept (b). For a vertical line, the slope is undefined because vertical lines rise indefinitely (up or down) without running horizontally. On the contrary, the slope of a horizontal line is zero because the line does not rise or fall as it runs horizontally. Since the equation given has no y term, it does not have a slope and therefore doesn't conform to the slope-intercept form of a line, which is y = mx + b.