Special Cases — Horizontal and Vertical Lines
Horizontal lines have equations of the form y = k, where y stays constant. Vertical lines have equations of the form x = h, where x stays constant.
Practice This ConceptMain explanation
Teacher explanation
In y = k, every point on the line has the same y-coordinate, so the line is parallel to the x-axis. In x = h, every point has the same x-coordinate, so the line is parallel to the y-axis. These special cases are important because one variable is fixed while the other can change.
Example
The graph of y = 3 passes through (0, 3), (2, 3), and (-4, 3). The graph of x = -2 passes through (-2, 0), (-2, 5), and (-2, -3).
Simple analogy
y fixed means flat; x fixed means standing.
Common confusion
Students often think y = 3 is a vertical line because it touches the y-axis at 3, but it is horizontal.
Exam tip
If y is constant, the line is horizontal. If x is constant, the line is vertical.
Answer writing and exam use
1-mark use
Write the exact meaning of special cases — horizontal and vertical lines in one clean line.
2-mark use
Define special cases — horizontal and vertical lines and add one example or condition.
3-mark use
Explain special cases — horizontal and vertical lines, show the method or example, and mention the common mistake.
Practice this concept with focused MCQs
Open the concept quiz intro first, review the test details, and then start a focused MCQ set from this concept only. Instant score and answer review are live now.
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