Algebra
Linear functions
Horizontal and vertical lines
20 practice questions
2 video lessons
Theory + worked examples
Theory
Two special lines hold one coordinate constant:
- Horizontal \(y=c\): every point has the same \(y\); slope \(0\).
- Vertical \(x=c\): every point has the same \(x\); slope undefined.
Horizontal has no rise (slope \(0\)); vertical has no run (undefined slope).
\(y=2\) is horizontal; \(x=-2\) is vertical.
The two special lines.
Slopes:
\[y=c:\ m=0,\qquad x=c:\ m\ \text{undefined}\]
A vertical line is not a function — it fails the vertical line test.
How to identify these lines
- \(y=\) a number: horizontal.
- \(x=\) a number: vertical.
- Horizontal slope is \(0\).
- Vertical slope is undefined.
Example 1 — Horizontal line
Describe the graph of \(y=3\).
Solution
Every point has \(y=3\).
| \(y=3\) | \(\Rightarrow\) | \(\text{horizontal line}\) |
Example 2 — Vertical line
Describe the graph of \(x=-2\).
Solution
Every point has \(x=-2\).
| \(x=-2\) | \(\Rightarrow\) | \(\text{vertical line}\) |
Example 3 — Slope of horizontal
What is the slope of \(y=3\)?
Solution
No rise, so slope is \(0\).
| \(m\) | \(=\) | \(0\) |
Example 4 — Slope of vertical
What is the slope of \(x=-2\)?
Solution
No run means division by zero.
| \(m\) | \(=\) | \(\text{undefined}\) |
Common pitfalls
\(y=c\) is horizontal, \(x=c\) is vertical — easy to swap.
Slope \(0\) is not the same as undefined.
A vertical line is not a function.
Frequently asked questions
What does \(y=3\) look like?
A horizontal line through \(y=3\).
What is the slope of a vertical line?
Undefined.
What is the slope of a horizontal line?
Zero.
Is a vertical line a function?
No — it fails the vertical line test.
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