Horizontal and Vertical Lines
Graph horizontal lines (y = k) and vertical lines (x = h) in Grade 10 algebra, understanding that horizontal lines have zero slope and vertical lines have undefined slope.
Key Concepts
A horizontal line has an equation of the form $y = c$ and a slope of $0$. A vertical line has an equation of the form $x = c$ and an undefined slope. A horizontal line and a vertical line are always perpendicular to each other.
The line perpendicular to the horizontal line $y=10$ and passing through $(5, 3)$ is the vertical line $x=5$. The line perpendicular to the vertical line $x= 2$ and passing through $(7, 4)$ is the horizontal line $y=4$.
Think of a flat horizon for horizontal lines—no slope at all, so their equation is just $y$ equals a number. Vertical lines go straight up and down, like a skyscraper, so their slope is undefined and their equation is always $x$ equals a number. Put them together, and you get a perfect cross, making them the simplest perpendicular pair!
Common Questions
What is the equation of a horizontal line passing through (3, 5)?
y = 5. All points on a horizontal line share the same y-coordinate, so the equation is y = constant.
What is the equation of a vertical line passing through (-2, 7)?
x = -2. All points on a vertical line share the same x-coordinate, so the equation is x = constant.
Why is the slope of a vertical line undefined?
Slope = rise/run. For a vertical line, there is no horizontal run (Δx = 0), causing division by zero, which is undefined.