HORIZONTAL AND VERTICAL LINES

LESSON READ-THROUGH
by Dr. Carol JVF Burns (website creator)
Follow along with the highlighted text while you listen!
 

Vertical and horizontal lines have equations that are simpler than all other lines!

Vertical lines have equations of the form ‘$\,x = \text{some number}\,$’.

Horizontal lines have equations of the form ‘$\,y = \text{some number}\,$’.

Why? Keep reading!

Since they're commonly mixed up, two memory devices are offered, so you'll always get them right.

Vertical Lines

The points $\,(x,y)\,$ that satisfy the equation $\,x = 3\,$ (that is, $\,x + 0y = 3\,$)
are all points of the form $\,(3,y)\,$, where $\,y\,$ can be any real number.
This is the vertical line that crosses the $\,x$-axis at $\,3\,$.

That is, in order to satisfy the equation $\,x =3\,$,
the $\,x$-value of a point must be $\,3\,$.
The $\,y$-value can be anything it wants to be.
To get to any of these points from the origin,
you move $\,3\,$ units to the right,
and then up/down to your heart's content.

As a memory device,
you might think of exaggerating the first stroke of the $\,x\,$
to make a vertical line.

Memory Device for Vertical Lines
Horizontal Lines

The points $\,(x,y)\,$ that satisfy the equation $\,y = 3\,$ (that is, $\,0x + y = 3\,$)
are all points of the form $\,(x,3)\,$, where $\,x\,$ can be any real number.
This is the horizontal line that crosses the $\,y$-axis at $\,3\,$.

That is, in order to satisfy the equation $\,y =3\,$,
the $\,y$-value of a point must be $\,3\,$.
The $\,x$-value can be anything it wants to be.
To get to any of these points from the origin,
you must move up $\,3\,$ units;
you can move left/right to your heart's content.

As a memory device,
you might think of exaggerating the $\,y\,$
to make a horizontal line.

Draw a rising sun to remind you of the horizon!

Memory Device for Horizontal Lines
HORIZONTAL and VERTICAL LINES
Let $\,k\,$ be a real number.

Equations of the form $\,x = k\,$ graph as vertical lines.
The $\,y$-axis is a vertical line; its equation is $\,x = 0\,$.
All other vertical lines are parallel to the $\,y$-axis.
All vertical lines are perpendicular to the $\,x$-axis.
Vertical lines have no slope; i.e., the slope is not defined.

Equations of the form $\,y = k\,$ graph as horizontal lines.
The $\,x$-axis is a horizontal line; its equation is $\,y=0\,$.
All other horizontal lines are parallel to the $\,x$-axis.
Horizontal lines are perpendicular to the $\,y$-axis.
Horizontal lines have slope $\,0\,$ (zero).
EXAMPLES:
Question:
Write the equation of the horizontal line that passes through the point $\,(3,-2)\,$.
Answer: $y = -2$
Question:
Write the equation of the line through $\,(3,-2)\,$ that is perpendicular to the $\,x$-axis.
Answer: $x = 3$
Master the ideas from this section
by practicing the exercise at the bottom of this page.


When you're done practicing, move on to:
Parallel and Perpendicular lines

 
 
CONCEPT QUESTIONS EXERCISE:
On this exercise, you will not key in your answer.
However, you can check to see if your answer is correct.
PROBLEM TYPES:
1 2 3 4 5 6 7 8 9 10 11 12
13 14 15 16 17 18 19 20 21 22 23 24
AVAILABLE MASTERED IN PROGRESS

(MAX is 24; there are 24 different problem types.)