Horizontal and Vertical Line Graphs

Key Questions

• A horizontal has the equation $y = b$ with $b$ any constant number
A vertical has the equation $x = c$ with $c$ any constant number

A normal linear equation is mostly of the form $y = m x + b$
where $m$ is the slope. In a horizontal graph, the slope is 0.
The $b$ (called the $y$-intercept) tells you where the graph crosses the $y$-axis.

For the vertical graph a similar story goes and $c$ is called the $x$-intercept.

$x = 0$

Explanation:

For any point on the Y-axis, $x$ is equal to zero;
furthermore, if any point for which the $x$-coordinate is equal to zero will be on the Y-axis.

• The x-axis is like a number line, isn't it? Every point on the x-axis has a y-coordinate of 0 like this: (-4,0), (3,0), (2.7, 0) and (0,0).

If all of these points have the same y-coordinate, it follows that the equation of that line must be y = 0! It would be the same idea for any horizontal line, since the slope = 0. Calculate the slope between any two of those points:
m = $\frac{0 - 0}{3 - \left(- 4\right)}$ using (-4,0) and (3,0).
You would write the equation now like: y = 0x + 0, or just y = 0.

Think about another horizontal line that goes through the points (8,3), (0,3), (-14, 3), and (4.1, 3). Calculate the slope:

m =$\frac{3 - 3}{- 14 - 0}$ using the points (0,3) and (-14,3).
The y-intercept is (0,3) and therefore the equation of that line is y = 0x + 3, or just y = 3.

• An equation of a vertical line can be written in the form

$x = a$,

where $a$ is a constant.

An equation of a horizontal line can be written in the form

$y = b$,

where $b$ is a constant.

I hope that this was helpful.