Horizontal and vertical lines
This Grade 6 algebra skill from Yoshiwara Elementary Algebra covers horizontal and vertical lines in coordinate geometry. Students learn that horizontal lines have the form y = k (constant y-value, zero slope) and vertical lines have the form x = h (constant x-value, undefined slope).
Key Concepts
Property 1. The equation of the horizontal line passing through $(0, b)$ is $$y = b$$ 2. The equation of the vertical line passing through $(a, 0)$ is $$x = a$$.
Examples The equation of the horizontal line passing through the point $(4, 7)$ is $y = 7$. Every point on this line has a y coordinate of 7. The equation of the vertical line that contains the point $( 2, 5)$ is $x = 2$. Every point on this line has an x coordinate of 2. The x axis is a horizontal line with the equation $y=0$, and the y axis is a vertical line with the equation $x=0$.
Explanation For a horizontal line, every point has the same height (y value), so its equation is just $y$ equals that constant value. For a vertical line, every point is the same distance left or right (x value), so its equation is $x$ equals that constant value.
Common Questions
What is the equation of a horizontal line?
A horizontal line has the form y = k, where k is a constant. Every point on the line has the same y-coordinate, and the slope is zero.
What is the equation of a vertical line?
A vertical line has the form x = h, where h is a constant. Every point on the line has the same x-coordinate, and the slope is undefined.
Why does a vertical line have undefined slope?
Slope = change in y / change in x. On a vertical line, the change in x is zero, making division by zero undefined.
How do horizontal and vertical lines look on a graph?
Horizontal lines run left to right, parallel to the x-axis. Vertical lines run straight up and down, parallel to the y-axis.
Where are horizontal and vertical lines taught in Grade 6?
Horizontal and vertical lines are covered in the Yoshiwara Elementary Algebra textbook for Grade 6.